If you are looking at trailers in the 21 to 23 foot range, there should be plenty available that have sufficient axle capacity. An example ( although shorter ) is my 19' funfinder. It weighs 3900 pounds ( that is total. There is 3400 pounds on the axles, ready to go camping ). It has two, 2800 axles, so there is plenty of reserve axle capacity.
I agree with the previous poster that pointed out the value of replacing existing tires with better quality. In the the 14" size, I am using Kumho 857, which is a "light truck, commercial" tire that they also market as suitable for trailers. With these four tires, I have 7496 pounds of load capacity, and as stated earlier, I have 3340 pounds on the axles. That means the tires are running at approximately 44% of their rated load capacity. I say approximate, because that would assume the trailer is balanced evenly left to right and on both axles, an honestly, most trailers are not. Point is, it is good to have excess capacity in reserve, for both axles and tires.
Shop carefully. Go to dealers, and crawl around under trailers to see what the axle capacity really is, rather than just believing what a salesman says they are.