Refinement for weapons is a fine concept, and can make an earlier weapon relevant for mid- and late-game. I think what that necessarily means is that each weapon type needs to be qualitatively different from one another. If a Lv 5 graviton beam has all features of Lv 1 laser beam, there will be no reason to use one of the two, depending which is more RP-efficient.
Yes, each weapon should be different. not just in how much damage it does but in the way affects the target. If lasers purely damage targets, then graviton beams should do something else, maybe they do damage and reduce speed. Lasewrs could do fixed damage at every range and another type of weapon would have reduced effect over range. This kind of thing would make the different kind of weapons much more interesting. In many kinds of computer games ion guns affect sheilds more strongly and temporarily disable the ship, rather than damaging it permanently (they also tend to be blue, with lasers red). I'm not saying we must have ion guns, but that SowerCleaver is right in saying that weapons all need to be different.
It also would mean that applications that are simple percentage boosts would not have refinements, as in those cases the applications themselves are essentially refinements.
An effort should be made to make technologies that just give numerical bonuses into refinements. Applications should, idealy, add something new to what an Empire can do, rather than just letting it do things better.
Technology which adds to mining for instance should be a refinement of an application which allows a planet to focus on Mining (which everyone should start with). A Technology which allows mining on asteroids would be a new application. Another example of mining boosting application, rather than refinement, would be something which adds to mining production on a world not focused on mining.
I still think that Applications should be able to have other prerequisties, so that it takes longer to research them. Maybe they should all have a long number of minimum turns, so that they don't come immediately after the refinement.
Having multiple refinements for a single technology is good, but they should if possible not just be +10%, +25%, +50% and so on.