Does it help if you build a cruiser or a battleship and choose all the "light" sections so it has 8 small weapon modules instead of two big ones? Or is it just the sheer size of the ship that makes it bad at taking down corvettes?
No no no... If you give them small weapons they need to go close to fight and you want them to fight as far away as possible. Otherwise they will be destroyed. Here is a general strategy.
Corvettes: THE SWARM. Anti-shield or shield penetrating weapons. Give them as high of an evasion score as you can (modules will help with this).
Destroyers: Carries some guns but also your point defense. Depending on who you're up against, you might not need that much pd, so I don't spend too much on it until I know i need it, and when destroyers fill that role I can build them all over the empire and rush them to whatever fleet ad hoc.
Cruisers: Ships of the Line. Simple but heavy hitting guns, medium range. The bulk of my conventional firepower.
Battleships: Crowd control and fire support. The most designs I have, because I bring every buff and debuff I can. 2, maybe as many as 3, of each effect if I can manage. Being costly and time-consuming, I give them defensive AI and only the longest range weapons to keep them out of range of most return fire, so tons of artillery and torpedoes as well as the extra point defense.