Utility Trailer Spare tire Sizes question

As I was thinking about it more, (if I'm correct?) ...the equlizer bar/triangle should distribute even weight to each tire on that side, regardless of the small difference in tire height, and being the hubs are independent (unlike a drive axle) the size difference shouldn't affect the larger tire on the other end of the axle

Good point as far as carrying the load. Many folks don't realize but when one tire goes flat its still carrying its share of weight through the equalizer bar. Thats why the flat tire shreds itself quick running down the road. And can start a beautiful spark show as it wears into a steel wheel at night.

A point on braking. Tires on a axle need to be fairly close to the same diameter for equal braking performance. Generally the brakes with the smaller diameter tire has a bit better braking performance as they are turning more rpms and may slide quicker under hard braking especially on wet pavement.
Also due to braking rotational forces the rear axle tends to lift the front axle through the equalizer bar which can lead to flat spotting the smaller diameter front tire on hard braking events.
I've used tires on my road trailers as much as 3/4" difference in diameter with no ill effects in wet pavement braking. I use the taller tires on the lead axle for that reason.