Welcome to the Forum.
At 1260# max load, those tires are only 50# above your trailers DRY weight (and this assumes 20% on the pin).
Previous owner is correct - you need higher capacity tires.
Look at the GVWR/Tire pressure label towards the front left side of the trailer.
What is the OEM tire size, load rating and pressure displayed on there?
THAT is your minimum starting point.
Most on here, including me, recommend bumping the tires up at least one load range to buy a little more safety margin.
Keith J.
Sold the fiver and looking for a DP, but not in any hurry right now.