Anyone still interested in this?
Generally yes, as long as we are talking "soft" limits; meaning that if your stat is below the required threshold, you can still use the item but with penalties (normally to accuracy). These penalties get progressively worse, the lower your relevant stat is. (The actual formula needs to be decided, I am not an expert on statistical curves.)
The reason for this is to allow weapons which are difficult to handle due to sheer mass. This cannot be done using stat bonuses, because it would make very strong units into perfect snipers with such heavy weapons.