None and none. Two reasons. First, the LSA weight limit chosen, 1,320lbs, is based on the European breakpoint (600kgs) for their version of Ultralight aircraft. It was done in the spirit of recent treaties with the European Union, and no one in Washington has any interest in bucking that precedent. Two, and most importantly, the LSA initiative was designed solely to spur the new production of aircraft. It just so happened that they couldn't find a way to exclude certain older aircraft that met the 600kg/1,320lb, GW limit.
The FAA does not have a single "study" in place to consider raising the weight limit. In fact, they specifically added the language "continuously certificated" into the authorizing language to knock out an already approved STC for Cessna 120 and 140's to reduce their gross weight to 1,300 lbs.
Unfortunately, the FAA doesn't have any interest in revisiting the GW limit. Mike.