Tire and wheel sizes have been standardized for some time now: Any 13 inch tire will fit any thirteen inch wheel--within reason. The 1-70 R 13 you can replace with 175, 75 or 80. You can probably even go up to 185-70 tires and still be 75 is width across the widest part of the tire when inflated, in millimeters. The 75 or 80 is called the aspect ratio and is the relationship of the tire height to the maximum width. Thus, an 80 aspect ratio tire will be greater in diameter than a 75 aspect tire. Too great an aspect ratio and the tire might not fit under the fenders.
Since very low aspect ratio tires are designed for larger width wheels, going to a 40 or 50 aspect ratio would crimp the beads together on a standard with wheel making it impossible for the tread to lay flat when properly inflated. SO: Since your trailer came with 175 70 R13 you can replace with 175, 70 or 75 R 13 and possibly 175 80 R13. You could also probably step up to 185 70 R13 and still be OK.
But really, 15 foot boats are carried on 8 and 12 inch wheels so there is no need for larger tires on your trailer. You already have plenty of load capacity.
