To avoid quadratic increase, I guess i'll have to disable the ability to upgrade structures (i.e reactors/turrets, etc) except for miner + mineral storage i guess since they dont contribute much to combat. The game was inspired by cosmoteer but the severe imbalance of free for all gameplay between varying ship levels made me add a peaceful mode with opt-in 1v1 pvp. And for 1v1 pvp, i did take inspiration from space arena. And i might take up your suggestion on certain weapons being effective against shields, and structure that improve turn speed, etc. Space arena plays very much like a single player game and idle game though, and you usually lose the match if you're ship is lower level in that game (although i havent reached like very high levels yet). But i think adding more types of turrets that counters other type of turrets/build can improve the strategy aspect of the game.
Yeah i do agree that space arena is also imbalanced level wise just using it as an example for ideas.
Don't take my advise too seriously btw, do what you feel is wiser, i'm by no means an expert.
As for upgrades maybe do them so they add a slight weight and energy cost increase, that's small yet considerable enough to make you consider upgrading everything to the max as soon as you have enough money.
Another idea i had for upgrades is instead using adjacency, for example parts that give a slight damage/range/reload boost to nearby guns or likewise. Another idea but probably more complicated to implement is to make it so that upgrading a part also forces you to make the part 1 square bigger in any direction you like.
Feel free to ignore or implement my ideas by interpreting, tweaking and or/mixing them however you think feels fit.