What is the gross weight limit for a Light Sport Aircraft? 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.