Is there any trick to checking in more weight on planes?

A couple of options spring to mind

The first is not to fly! Take the train - either TGV in the daytime, or the Trenhotel sleeper overnight, plus onward Spanish trains as needed. You can basically take all the luggage you can physically carry. Book in advance and you can get a bed in a 4 berth cabin from Paris to either Madrid or Barcelona for only €80, and on the daytime trains in advance it's about €40 from Paris to the border, then another €20 onto Madrid.

Again with not flying, why not ship your stuff? Takes a while, but it's fairly cheap usually. Look out for adverts in studenty places.

Next option, some airlines will let you pre-pay for excess baggage in advance, usually online. You do have to pay, but it's generally a lot less than at the airport.

Another option is to fly business class rather than economy, as you normally get a much better bag allowance. For example, BA let you check one suitcase up to 23kg in economy (euro traveller), but in business (club europe) you can take two suitcases each up to 32kg!

Finally, the onboard weight limit isn't usually checked. If you can carry it, and the bag is small enough (it's usually size they check) then you can normally get away with it.

The only 'tricks' I can suggest are four methods:

1) Put dense, heavy items in your carry-on. I travel a lot, and am hardly ever weighed. Until my most recent Auckland -> London flight, when believe it or not, I had 10.5kg in my carry on, when the limit is 7, and Murphy's Law - they weighed it, first time I've had that in 10 years. We looked at each other, I acted awkward and surprised and pointed out my laptop was in there and was heavy, and my medication was in there too. She asked if I needed it for the flight, I said yes, she was relieved and waved it through :)

2) Duty-free bags. If you can get some, or get your carry on through - even if you're only allowed 1 bag (looks in RyanAir's direction) you're still usually permitted two duty free bags on even lost cost airlines (I use this example from Madrid to London, where there are signs pointing out this fact next to the duty free shops). Those won't get weighed.

3) Devious and you're stuffed if they check again - but you can get a friend to hold heavy stuff from your carry-on until you've had it weighed, and then put it back in. But if you're under supervision, this would surely raise all sorts of alarm bells!

4) If you're really desperate, despite all the weighing of bags and carry-on, most airlines don't weigh people - check to see if yours does (eg. Samoa Air does now). As such (and I've seen this done) you can wear as many layers as humanly possible, reducing your luggage - and of course, you can take most of them off on the plane ;)

Bonus fun fact: 11 years ago using carry-on and tourist bags from Hollywood, a friend and I took an entire stereo system, including speakers as carry on :D

It's easy to carry more with you, just pay the fee... And yes, that's the only answer I'm going to give as I'm sick of people trying to board aircraft with massively oversized and overweight luggage (especially cabin luggage), causing delays as things have to be rechecked, rebagged, thrown out, fees paid at the cabin door and paperwork filed, overhead bins stuffed to capacity before half the passengers have boarded, etc. etc.
Extremely selfish behaviour putting yourself over everyone else like that.

Here's a link that shows an example of how you can bring more weight on the airplane by bringing a jacket and stuffing it with items. He seems to have quite a bit of luck with it. At first glance, it seems shady, but it still goes through the x-ray like all the rest of the luggage, and he isn't carrying anything weird or illegal.

What airline are you travelling with?

I've used Ryanair a lot and they are cheap but they are very very strict with excess baggage, and will usually charge fully amount for every kilogramme over the limit. However I've flown Aer Lingus and they are usually a bit more flexible when you check in. Get to the check in desk nice and early and make the clerk's job easier by having all your paperwork in order, and be friendly.

I typically travel with a checked bag very close to the 50pd limit and then have a carry on and personal item. My carry on is my camera bag loaded down with 2-3 cameras, assorted lens and other camera goodies. My personal item is a laptop case with 1 or 2 17" laptops. Because my camera bag has lots of extra snaps and buckles I can typically attach an additional bag to it be it duty free, a purse, whatever.

So, I'm carrying an additional 30 or more pounds as carry on. As another poster said I've never been weighed and I've not had my carry-on baggage weighed. And, my bags while heavy always fit in the bins or underseats. So, for your carry on perhaps pack the smaller, denser items there to free up some weight space in your checked bag.

I remember a recent flight out of mexico my bag was too heavy and paying extra wasn't an option so they opened my bag and asked me what I could carry. I was able to strap stuff to my camera bag but I'm sure it was interesting looking.

With international flights heading back to the US double check bag information, often you may be able to travel home with two checked bags for no additional cost.

Three tips that have helped me get more than the weight allowance on a flight: use a duffel bag, be friendly, and try a different check-in agent if the first one doesn't work.

I recently traveled on American Airlines and LAN from Washington DC to Cusco Peru. I had a 69 lb suitcase, a 58 lb duffel bag and 15 lb backpack and a handbag. I was concerned at having to pay for two overweight bags at $100 each according to AA's website. I knew the minimum fee would be $30 for one extra bag (AA gives you one 50 lb bag for free on international flights).

I prayed to the travel angels and smiled and kept a positive and friendly attitude with the ticketing agent and struck up a friendly conversation with her. And when I put the duffel bag on the scale the ends must have been drooping off the edges of the scale because it only showed 42 lbs! The suitcase showed the whole 69 lbs that I was expecting so the scale wasn't broken. Then the agent researched the fees and discovered that instead of paying the $100 AA overweight fee I could pay the $90 LAN overweight fee. Yippee!

Update: My flight was canceled and I had to return the next day. I could have left my bags to travel without me and picked up in Cusco but I wasn't keen on leaving them at the carrousel in Peru for hours without me so I took them overnight to a friend's house and checked back in the next morning at curbside. This agent was not so friendly and he put the duffel bag on the scale himself end up instead of me putting it on with the ends hanging over the edge. The true weight of 58lb showed. I asked for a break due to flight delay and when he said no I just went inside to check in at the ticket counter instead. This time I showed the agent that I have already checked in and had luggage tags - she just printed new ones and put them on without reweighing. So sometimes it pays if you don't get by the first agent to try another one...

OP, I think you are mis-interpreting the conditions of carriage.

You are "allowed at 23Kg checked-in and 10Kg on board" for free, but you are also allowed more checked baggage for an extra fee. The number of checked items and the fee per item depends on the airline - typically low-cost airlines allow less and charge more - but some airlines are quite generous. For example, KLM allows, on many lines, up to 10 checked items. A couple of years ago I asked a question here on the site on the practicality of actually doing something like that.