How does the new 'Weight' Feature work? [duplicate]
The lighter your load, the faster your powers cool down. Different classes have different max carry capacity, and you can boost it through upgrading their passive class ability. The biggest bonus to power regen speed you can get is +200%, meaning a 9 sec cooldown will be reduced to only 3 seconds. Soldiers and Vanguards, I believe, have the highest weight capacity, while Adepts and Engineers have the least.
As a Sentinel, I've managed to carry along a shotgun, an assault rifle and an SMG (Just for kicks, as they are pretty much weightless with the proper mods and upgrades) while maintaining a respectable power regen bonus (+180% or so).
Squadmates are unaffected by weapon weight, so feel free to pack them with heavier weapon variants.
Sniper rifles are the heaviest weapons, followed by shotguns and assault rifles. Pistols and SMGs are fairly light with a few exceptions. SMG weight can be reduced to nearly nothing with appropriate mods and upgrades. There are a few light assault rifles, which also tend to be fairly accurate and stable, making them ideal for Shepards.
You have slots available for all of the basic weapon types.
See here for a discussion of what the basic types are.
You add the weight of all the selected weapons together, and compare it to your carry capacity. If it is below your capacity you get a bonus to your power recharge speed. If the weight is above your capacity you get a penalty to your recharge speed.
Your capacity can be increased as part of your skill regression for you class. You will absolutely need to take this upgrade if you want to carry heavier weapons as an Adept or Engineer.
You can decrease the weight of weapons slightly by upgrading them(i.e. Mantis I => Mantis II) in the shuttle bay. Sub machine guns have an attachment that can reduce their weight up to 90%.
As an Infiltrator, with the increased capacity skill, I was able to carry a Black Widow sniper rifle, Vindicator assault rifle, and a Tempest SMG with the weight saving attachment.