There's no limit to the weight of carried equipment, but there's a limit to its amount (150). While it isn't much problem at the beginning, later you have to watch out for not to be forced to leave or turn into omni-gel useful parts of your equipment. I propose to exchange them to more advanced ones systematically. Older, worse objects could be disposed in two ways: sold or disassemble to turn into omni-gel. Every object give the same amount of omni-gel, so it's better to sell more expensive equipment and disassemble cheaper ones. This way you won't run of money and omni-gel alike.
While your character gain new experience levels, you can get more advanced equipment. Objects found at the beginning of the game have little value and it's not worth keeping them in inventory in order to sell. Turn them into omni-gel instead, which will be useful later.
Hint 1! It pays to sell objects found approximately after 20 experience level.
Hint 2! Really valuable objects are not possible to get until 50 experience level. Try to complete side quests and gain as much experience points as you could and you will be able to achieve it near the end of the game. This way you could use solid equipment with lot of slots for upgrades.
As for weapon upgrades, I suggest to change tactics a bit. Remember, that some ammunition types are better against specific opponents, so you should be prepared to fight humans and aliens as well as synthetic geths. During combat, you can freely change weaponry configuration, so there's no problem with switching ammo types. In general, it's always good to have within reach upgrades which results in major injuries of synthetics beings, of organics beings and which let you go through the shields.
As for armor: before you get better one, which lets to mount more than one upgrade, you should mount upgrades that cure you automatically. This way your health will be constantly regenerated, not only during the combat.
Remember, that shops' assortment changes in course of the game. It goes by leaps: after gaining 18 experience level, after unlocking achievement Rich (accumulate 1,000,000 credits) and after gaining 50 experience level. It's not hard to guess that after the last change you could buy the best equipment: powerful and tough armors with strong shields as well as precise and deadly weapon.