Pay careful attention to the tongue weight rating on the trailer hitch (not infrequently on class C's it's lower than you might expect for the stated tow rating) and the rear axle weight limits. Due to the long overhang, the tongue weight will tend to shift weight to the rear axle, so its weight will go up by more than the tongue weight, maybe approaching double in some cases. It depends on the ratio of the rear overhang between the axle and the hitch and the wheelbase.
Based on some quick searching, I think this would mean trailer weight somewhere in the vicinity of 2000 pounds, assuming an open trailer. It should be doable with many class C's if proper care is taken. Backing a short trailer with a long tow vehicle that has less than great visibility is not the easiest task in the world, of course.
