Being a Marlin-era gun the chambers are most likely 2-3/4", as the transition from 2-9/16" happened in the late 30's.
Skeetx's suggestion about glass-bedding the head of the stock is almost a must, as (from the pics) there appears to be a sizeable gap between the back of the lockplates and the stock. In addition, the head of the stock is probably oil-soaked, as the gun appears to be heavily used (very worn checkering).
Light 2-3/4" loads would be OK----AFTER you glass-bedded the stock, but if you do more research you can find nicer Hunter 16's than this one for a little more money-- just MHO.
