In the TNG episode Heart of Glory, Worf says the enterprise separates its saucer because "when relieved of its bulk, it becomes a formidable weapon." So large capital ships lack the maneuverability and battle usefulness of smaller ships which are more maneuverable. Clearly, size and weight are important in trek space warfare.
And that's because Star Trek is, supposedly, set in a real universe with real, basic laws of physics.
The amount of energy to move a 1kg mass is always going to be 1/2 of the amount of energy required to do the exact same thing, in the exact same way, to a 2kg mass.
You can also think about "armor" (in this case, shields, but the same concepts largely apply to both). Imagine that a shield is the equivalent of 1" thick armor plate. For real armor, plating a small craft adds much less mass, and thus results in a much lighter vessel overall, when compared to a larger vessel.
In Trek, we're not talking mass, but we ARE talking about energy. The amount of energy required to generate a certain degree of deflector/shield protection for a small craft is much, much less than that required to generate the same level of protection (in "inches of armor equivalence" I suppose?) for a larger vessel.
For a "fighter," we're basically talking about needing a small, light propulsion system (not designed to run continuously and not required to have many levels of redundancy). We're talking about a much less power-intensive shield system, not required to protect an entire large vessel, just a small craft. We're talking about a lot less energy to maneuver.
SO, to get the same amount of weapons-capability, you only need a generator able to output as much energy as is required to put out the desired level of weapons fire, plus JUST ENOUGH energy to move it around and provide basic protection. It's a far more efficient method, all other things considered.
Now at the outset of TNG, we saw only big craft, but by the end of DS9, and the Dominion War, this had largely gone by the wayside. We never see "fighters" per-se, but we hear about them a lot. We hear about "carrier groups" as well. The SFX shots were limited to what they already had to work with, but the SFX shots also showed ships a few meters apart when dialog puts them millions of kilometers apart, too, doesn't it?
I'd say that at the outset of TNG, there were very few fighters... because the Federation was convinced that it was "at peace in a nice, happy-friendly galaxy."
Q showed them otherwise, by introducing them to the Borg (presumably, the Borg were already headed to meet them and he was just giving them a hint of "early warning" on a threat which was rapidly approaching).
And then the Dominion War put all that pretense to an abrupt end.
When you're designing ships to fight a war, as opposed to ships of exploration intended to be able to defend themselves in a pinch, you take a dramatically different tact.
By the way, I keep putting "fighters" in quotes, because of exactly what Timo said above. But his point isn't entirely accurate, either.
He's talking about "interceptors" as though they are "fighters"... as though the two are synonyms. But I'm sorry, the F-15 Eagle is a "strike fighter" and the F-111 was a "fighter/bomber" and so forth. And "weapons" need not be limited to "bombs and missiles"... the Warthog deploys a cannon as its main armament, not for anti-fighter use, but as a ground-attack weapon, just for example. This is why I use the broad, generic term "weapons platform" instead of "bomb deployment platform" or "50mm canon round platform" or so forth. Just "remote weapons deployment platform."
In "Trek" terms, I think that there would be no real difference between "fighters" (including subcategories like strike fighters or interceptors or the like) and "bombers." I'm not using "contemporary terms" as much as I'm using "practical logical definitions."
A "fighter" is a remote weapons deployment platform... which can be a phaser-gunboat, or a heavy torpedo-launch platform, or an interceptor to deal with incoming missiles or fighters, or the like, as I'm using the term. The point is to intercept and engaged a hostile force (whether capital ship, stationary base, or small craft... or some combination of the above) before that force is able to engage your primary base of operations (whether it be a capital ship or a stationary base).
That's what the term means as I'm using it here, and what I think we all should be using.