It really depends on the Class C. I see the Mazda 3 has a weight range of 2,865 to 3,028 lbs. Some Class C's do not have a 5,000# hitch and might be 3000 lbs. or 3500 lbs. Key is to know your vehicle weight, the maximum hitch rating, then you can get a weight for a dolly or a trailer and see. You'd be hard pressed to find a trailer for less then 1000 lbs, so that might change which Class C you buy.
That was a factor for us when we went to our Class A, I was finding most Class Cs didn't have a 5,000 hitch rating or enough capacity to tow that much weight.