I don't think it matters much what class we would assign any particular fighter, since whatever rule we have for this we will find exceptions to; but I do think categorizing by mass is simple and insightful. If we leave dedicated bombers like the Tally and Eclipse aside, but include fighter-bombers like the Vanguard and Gladiator, broken down by weight class looks something like this:
Light
X-85 8k
Blade 10k
M-50 12k
Bucky 14k
Mustang 13-17k
Kartu-Al 15k
Gladius 16k
Medium
Hurricane 16k
Sabre 18k
Avenger 18k
Heavy
Defender 18k
Tana 19k
300 series 20k
Hornet 22-23k
Fighter-Bomber
Gladiator 26k
Vanguard 40-52k
Gunboat
Redeemer 42k
These classifications in history have varied widely in use, even by those in the same service. It is like the term "Corvette" or "Destroyer" in that each time it is used, it is redefined. Is a Corvette the smallest "ship of the line" or the largest ship that is not yet a "ship of the line"? No one knows, but everyone thinks they know. Same here.
What is more important than the classification is to note the general purpose of a given group and ask how well any given fighter performs in that group. Light fighters are intended for mass attacks and throw away. That's why TIE fighters have no shields. One hit and they are down. Most of these Light Fighters are this way, but so is the Hurricane, so why would I say the Hurricane is a Medium Fighter? Well just because! I think it hits too hard to be a "Light" fighter. F-16 is a good example of this class in today's world.
Medium fighters are generally where you will find the "air superiority" or in our case "space superiority" fighters, intended to go to combat with anything else and win. The F-22 is an example of this. While it cannot carry large amounts of ordinance, it can turn circles around pretty much everyone else. It is there to win, and sacrifices multi-mission capability to do so.
Heavy Fighters have traditionally been long range and "multi-mission" fighters like the P-51, F-4 and F-18. They are the ones who carry the hard hitting but not quite bomber type loads, and are most often fitted with electronic warfare packages like the F-18 Growler.
Fighter-Bombers are not much in use today, but the F-111 was a near perfect version of this small bomber. It is probably no surprise the Vanguard looks like an F-111 because that is what a real fighter-bomber looks like.
Gunboats are rare these days, and really have more marine corollaries than in the air, but once upon a time, US air strategy included gunboats intended to shoot fighters out of the sky. During WWII, the fabled P-61 "Black Widow" widowed many by its use of advanced radar used to track, hunt, and kill aerial targets. The P-61 was famous for finding it's prey at a time and place were simple darkness ought to have been enough for concealment, and those birds justified their unusual size by the need to carry the air-to-air radar. They were big, but they were as nimble, fast and had as much range as the fighters they stalked. Its chief advantage was it knew where it's prey was before it's prey knew it was coming for them, so encounters were short. That is, all its encounters save those with the Foo Fighters, which to this day no one understands nor can explain.