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.