15" wheels and standard issue tires ??
Well I see ;
ST205/75-15 load C and D at 1820 -2150 lb respectively. A upgrade to D or E below is good.
ST225/75-15 C/D and E at 2150/2540/2830 lbs. And of course D and E is a good upgrade.
If your trailer has 6 lug axles a upgrade to 16" wheels and a ST E or LT E s a good upgrade. You don't need a 16" load G at 4080-4400 lb on that small trailer.
You sure don't want a 17.5" tire and wheel at 4000-6000 lbs/110 psi to replace a 15" tires on a small trailer. Those tires require a 8 lug wheel and are better suited to heavy trailers.
A trailer with close spaced axles unlike a truck with axles towards the corners can have too much tire.
Give us your trailer OEM tire size and load range and the trailers axle ratings and we can give you some good tire sizes/load ranges and brands recommendations that seem to work better.....and some that don't work the best