upgrading tires on a NT 22fbs

I have upgraded tire from the stock Duros 205/75/14 c rated to maxxis radial st tires(same size), but the trailer has quite a bit of sway when towing. I know they make a few d rated 14" tires but, if I went to D rated tires in a 15" would the stronger sidewall help with the sway? I also would like to get the trailer a little higher off the ground, we have had an issue with the rear stabilizer jack pads snagging while backing it up in our workshop. Would the height cause a negative change in handling?

I know this is off topic but, we have an 2011 F-150 4x4 with an Equalizer brand hitch. I have upgraded the rear tires from p to lt on the truck, & still having issues. We have added/ removed washers, change height of the leveling bars. It will seem to pull good one time but bad the next, seems it always windy while we are traveling, so it may just be, with the trailer being longer & lightweight that nothing will fix that.

I am not familiar with the equalizer hitch, does it have a built in sway bar? Or do you have a sway bar?
If you have good tires that are balanced and proper amount of air, and you have the trailer level when hiched and a anti-sway mechanism, you should be good. The only other issues I can think of might be axle alignment, (but you would have seen poor wear patterns on the old tires) or possibly too much weight in the rear of the trailer (although the equalizer should bring the trailer back to level).
Our trailer also sits very low to the ground, not a big issue for us, but would be more convenient to be higher. Would like to see some replies from others if there is a way to improve it without major work or expense.

It is important to make sure the trailer is level when towing. If the front is high at all it can cause sway.The trailer tires should also be inflated to the maximum pressure. Having changed to an LT tire on your truck be sure your truck wheels can handle the extra tire pressure they use. I towed with an E-150 using an Equal-Izer hitch and it was fine using the stock tires on the truck. I have use a couple Equal-Izer brand hitches and had very good results once they were set up correctly. If your trailer tires meet the weight requirement of your trailer they should be fine. Maxxis is the preferred tire in those smaller sizes. My guess is that you may be lacking in tongue weight. More is better than less. A trip through the scales may help determine what your actual numbers are. There is an excellent video on setting up your hitch on the Mfgs. website. The bars should be parallel to the tongue, the rear of your truck should be set to drop about an inch and the front should remain about the same height loaded or unloaded. It takes awhile to set the hitch correctly and it will work very well once it is done. Good luck ...Don

After an axle problem with my NT 21 FBS the replacement tires I put on were 215/75/R14. Little more weight capacity. Balanced when I put them on the trailer. Have taken just one short trip with them so far and all is well. Tires are Tow Master from Costco and made in Indonesia. The Reese dual cam sway control hitch is on it's third trailer and 23 years old. Gives very solid ride.