First off, have any of you played the Advance Wars games (turn based strategy)? In the earlier games, your character you chose could make a pretty big difference in what you did, and it was common for balance to work sort of like this: +20% attack power for X type of unit and -10% for Y. There were others who had +10% X and no real weakness, and I think that would be a good system for perks, and Heavy Armor/Light Armor is a good example. Light armor boosts health by 10, no drawback. Heavy armor boosts health by 20 but lowers your speed. Improved melee could result in slightly longer weapon switch times, Focus upgrades could result in a slightly slower melee attack, so on. Btw, I know that's a terrible idea but I needed an example. Things like stabilizer or Improved upgrades (melee aside) would have no weakness.
Like I said, I'm only talking about the concept, not execution (my bad ideas/examples).
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