Can I tell if the airline sold "my" seat after I cancelled the return leg after partially traveling?

Well, it just doesn't work like that.

No, they will not re-sell your ticket because even though you cancelled part of your itinerary, your ticket likely still has value. They are two different things and your ticket is still yours.

The value remaining on your ticket is the total of the ticket prices of the cancelled segments.

If you purchased a non-refundable fare, which is different from the ticket by the way, then they will not refund any of that to you but you can still apply the remaining fare, minus a fee, to any future flights purchased through BA.

Whether any flight goes out full or not is totally irrelevant to the value remaining on your ticket. Also, your seat assignment has nothing to do with your ticket either.

Speculation.

You booked a TLV-MEX fare on BA on the understanding it was refundable. The standard refundable or partially refundable economy booking classes on BA are Y, B and H, the cheapest of those, being H.

A sample TLV H fare on matrix is fully refundable:

REFUND WITHOUT PENALTY PERMITTED AT ANY TIME

This half-round trip fare is $830, plus YQ and fees.

The next most-expensive booking class normally in the non-refundable category is K which carries (in this particular sample case) the following conditions:

CANCELLATIONS
BEFORE DEPARTURE
CHARGE USD 100.00.

However, after departure:

AFTER DEPARTURE
TICKET IS NON-REFUNDABLE.

This half-round trip fare is $698, plus YQ and fees.

Without knowledge of the fare basis you booked, it's not possible to determine the exact fare rules you are subject to. However, I suspect that you might have booked a refundable fare, providing you cancelled before departure. After departure, this fare became non-refundable apart from government taxes and airport fees.

If you are certain BA told you this was completely refundable at any time, you may be able to ask them to retrieve the recording of the phone call and determine whether this was the case or not. If this is possible, BA may offer you a refund based on the guarantees given by the BA phone agent.

As a point of comparison, raising the cheapest non-refundable fare (S) to a refundable (H) fare took the return price from US$965 to $2070.

Disclaimer: this is from my personal experience as someone that used to work for fare calculations at a decently big airline (star alliance member)

The refund amount for a partially used ticket is calculated by your ticket price - oneway price of the segment you used - any refund penalties.

You mentioned multiple times in comments you have done the math and it is different than the airline's refund quote. I have heard plenty of travellers thinking that oneway price used in calculation is just (round trip)/2, hope you are not one of them.

Also I dont think anyone mentioned this: when refunding round trip ticket, the one way fare is calculated using the same fare class or higher.

Example: passenger bought an H class roundtrip to be eligible for refund for $2000, he saw than one way is $1000, but what he didn't know is that one way is a K class while the H class one way is $1500. And he argued with me that the refund should be $2000 - $1000 - $200(penalty) while the correct calculation is $2000 - $1500 - $200.

Again this is all from my previous job at the star alliance airline, the calculation method and such could be completely different at BA.

How did you calculate the refund due? Did they tell you a specific amount or have you done your own calculations?

If you did the math, did you take into consideration that cancelling the return portion of a round trip ticket will cause the original flight to be re-priced as a one way ticket, which is often higher than half a round trip. This would cause the amount refunded to decrease considerably.

Did you include costs for change fees when doing the math? Did you upgrade to a fully refundable fare or a limit refund fare.

There are so many factors that go into ticket pricing, that it is hard to blame any one item without all the fare specifics and penalties.

Out of curiosity I went onto British Airways to see the difference in round trip vs one way trips.

Round trip prices was around $1000 total. ($500 outbound and $500 inbound).

Looking at one way trips the only option they gave was a "World Traveller" operated by BA which had a ticket price of $3,000.

This date was just chosen at random (but was the same outbound date for both) but it shows what a discrepancy between round trip and one way prices. If you cancel halfway through you end up paying the one way price (or just get no refund if the one way price is higher then round trip I would assume).

Imagine you bought some 2 shirts on sale for buy one get one free. You decide you don't like one of the shirts so bring one back. You would get no refund on the shirt because then you would have to pay the full price for the shirt you kept even though you returned half your purchase.

Round Trip

One Way

Ticket pricing is extraordinarily complex. First of all, all airlines sell tickets via various travel service companies, and possibly via the online aggregators (booking.com and whatnot), and direct. All of these channels have different prices because they cost the airline different amounts to actually fill the seat. Which method you used to buy the ticket in the first place affects price, flexibility and refund potential.

Secondly, ticket prices vary by time of flight, departure/arrival location, and the point in time you buy it - in general, the more in advance you buy it, the cheaper it is. However, that's not always true - in some cases airlines will sell tickets cheaply shortly before a flight leaves in order to fill seats (and maybe make money, maybe contribute to costs). That's not always true, I guess because they figure you'll either pay more to go right now, or pay more on the next (not discounted) flight.

There are a bajillion other variables too. Some destinations are major tourist locations, so airlines run 'Saturday change-over' flights, but few other flights in the week. Such patterns are to cater for weekly/fortnightly holidays and such like. As a made-up example, flying to the holiday island of Blowyernose is very popular, but apart from a handful of locals, most of the people on the island are either tourists or workers. Most workers live on the mainland and come in by boat. As such, the demand for seats leaving Blowyernose is almost exactly the same as the volume of seats arriving there.

Let's say you fly to Blowyernose, but decide to cancel your return (and instead take a boat to the mainland and fly home from the mainland). In this case, the airline is unlikely to be able to re-fill your seat at any reasonable price (because all potential customers already have return tickets). As such, they can either sell the seat at a loss, or fly with it empty. You'll be expected to pay them for their loss here. You'll find that flexibility (especially on the return leg) is likely to be relatively expensive on these sorts of routes because of the illiquid nature of the passengers it carries.

Conversely, flying between two major hub airports is a bit like a bus service. So many people do it that it's easy to resell your seat (seats are a very liquid product here). In such cases, the airline can resell your seat to someone else and still charge you for it (they make money here, so will sometimes be more willing to share it by making flexible tickets relatively cheaper on these routes).

There's another complication here though... 'resell' can mean different things. It may be that another person on a fully flexible ticket turned up at the airport early and asked to fly sooner than they expected. They can sit in your seat, but that leaves on empty on the later flight. In some sense then, the price you paid for 'your' seat actually is apportioned to the later flight. Things get really complicated when you start to think about the flexible fare might have been based on a cheaper (or more expensive) flight than the one you were booked on, and exactly what does your ticket price subsidise?

In short, tickets get sold with rules. Those rules are pretty clear about what happens in certain circumstances, and these days, that usually means customers have to pay an 'admin fee', or forfeit the cost of the ticket, or something else that means your wallet is somewhat lighter than you think it should be. It happens to us all at some point, but one way to think about it is to consider the various alternatives and their cost (to you). Could you have bought a more flexible ticket (presumably more expensively) and got back some fraction of its cost and been better off? It's difficult to get exact numbers because of the transient nature of ticket prices, but it seems unlikely to me.

Can I tell if the airline sold “my” seat after I cancelled the return leg after partially traveling?

No, and I won't go into details since that is not your "real" question. You are looking for facts to go to court. The question who sat on your seat does not factor into this on any level at all.

Regarding this angle: forget about it. You have nothing except your memory of a phone call. Even if you had a recording of that call, no court will admit such a recording as evidence. You did not even get a quote on how much your refund will be.

The good thing: you spent all that money on experience. Now you know to get everything in written form up front, and if that is not possible, then do not expect it to work at all. The same goes for insurances and similar businesses.

This is not meant as a snide remark, sometimes it just does not work out.