Can I use any route to get to my destination on national rail?

(this post assumes you are on a regular rail ticket that is not route or operator restricted, oyster/"contactless" has it's own rules, which may be more or less restrictive than a regular rail ticket)

Can I use any route to get to my destination on national rail?

No, you can't just take any route.

Unfortunately the rules on what routes you can and cannot take are a hellishly complex mess as the railway tries (and sometimes fails) to strike a balance between allowing people to take reasonable routes and forbidding people from taking unreasonable ones.

My advice for a regular traveler is to look your journey up on national rail enquiries or another site that sells UK rail tickets (national rail enquiries is the most official, but their site seems to often bug out if you try to specify more than one via point, also after adding a via point the page reloads, but it doesn't actually update the train times until you explicitly tell it too) and see what it says about tickets for your journey.

If you get a warning about "some journeys require multiple tickets" on a national rail enquiries search, then pop down the "other tickets" button for the journey you are interested in to see if that particular journey can be completed on a single ticket.

For example, If I was at Surbition station and I wanted to get to Richmond Station could I take a train to waterloo and then to Richmond

That seems to be ok.

or take a train via weybridge and then go to Richmond

When I did a search with "via weybridge" it seemed to come up with journeys via weybridge and virginia water, which it thought were ok on one ticket, but also a journey via woking and clapham junction which it thought was not ok, Presumablly because of the rather large doubleback.

In the case of major disruption the usual rules are sometimes relaxed. You would have to check train operator websites or ask staff to be sure.

As a rule railway companies do not allow you to overshoot your station and return to it, although you often do not have to pay extra if you find out that your train did not stop where you expected it and you need to return to that station. They may charge you with an 'traveling without ticket'.
(Added after reading the other answers:) It turns out that in the UK you may overshoot and return more often than in most countries, but within limits.

There might be exceptions to this rule, where overshooting and returning is so much faster or easier that they allow people to travel that way. In that case you should either find a printed (or online) source and have that handy when you travel that way or ask a train official about your intended travel and make sure you are allowed to do what you want to do.

And also, train companies in the UK often print on the ticket which train companies and/or which routes you are allowed to use.

When you get an 'all permitted routes' or some sentence like that, you must use a logical route which is as direct as you can make it. So no overshooting and returning.