My fault, assumed it was the trailer for that boat. Yea, 13" is kinda small for that weight, IMHO. If you're not in a hurry for tires, I would shop around for the best deal. Sometimes manufacturers ( and some dealers) will have a pretty good discount, like $80- $100 off if you buy 4. If you can go 14" - 15", I would consider the Endurance tire but I know sometime price dictates what to buy. Tire Rack has the Endurance for $108 shipped to your choice of installer. That's not on sale just their price. Had mine shipped to NTB & they charged $40 ( all 4) to mount, balance, & valve stem. Not bad really. This a fairly new tire so any of them you get will have a dot date of 2017. But check with Tire Rack for whichever tire you choose, they usually have good prices, but again shop around. Good luck & good fishing. BTW, no, I'm not in any way shape or form associated with either of them. Retire LEO that just likes to fish.
Cheers