A Contractor's Character Sheet has a space to detail their Equipment. Players manage the contents of this field and can bring anything their Contractor could reasonably gain access to.
Restricted objects such as drugs or military weapons require the Stockpile or Arsenal Assets.
Some GMs may be charitable, but in general if your Contractor doesn't have it written in their Equipment list, they don't have it.
Carrying a small amount of gear won't typically cause any penalties, but if you bring too many things, you will become Encumbered, and your ability to move around will be restricted.
Some Games and circumstances may dramatically restrict a Contractor's access to their Equipment. They may be teleported to the site of the Game in their pajamas, for example. This is entirely fair and acceptable. Powers that take the form of unique items may be stripped or stolen just as easily.
All standard movement, Combat Actions, and rolls assume that a Contractor is carrying some amount of weight, such as a backpack or satchel. If a Contractor is totally unencumbered (i.e. carrying nothing but maybe a small object in their hand, plus their clothes), they receive a +1 dice bonus to all physical Actions.
A Contractor can carry 15 pounds per point of Brawn with no penalty. Once they hit that limit, they are considered Over-Encumbered, and take a -1 dice penalty per 25 pounds over their limit.