In the US, I see a lot of LSAs stating their take-off or gross weight limit as 1320lbs. Can some of these planes have a higher physical limit and that 1320lbs is just more a category limit?
Yes, 1320 pounds is the regulatory Gross Takeoff Weight for Light Sport aircraft.
From the AOPA website:
Light sport aircraft are defined as simple, low-performance, low-energy aircraft that are limited to-
1,320 pounds maximum takeoff weight for aircraft not intended for operation on water; or
1,430 pounds maximum takeoff weight for aircraft intended for operation on water.
1320 pounds is the weight limit for land-based LSAs, or 1430 pounds for sea planes. The regulatory definition is in 14 CFR 1.1:
Light-sport aircraft means an aircraft, other than a helicopter or powered-lift that, since its original certification, has continued to meet the following:
(1) A maximum takeoff weight of not more than—
(i) 1,320 pounds (600 kilograms) for aircraft not intended for operation on water; or
(ii) 1,430 pounds (650 kilograms) for an aircraft intended for operation on water.