How do I find out if the floor joists could hold additional weight. The exterior walls are currently 2x3 and not 16 on center, it is amazing this type of wall structure passed inspections when it was originally built. We need all new insulation, so we decided it would be better to change the studs to 2x4s for extra insulation. Question is how to know if the floor joists are strong enough to hold the extra weight? They are about (exact measurement) 5 1/2 x 1 1/2 and approx. 20 inches on center. The outside measurement of the trailer is 12 feet wide x 55 feet long.

Background, we had a huge family but we lost a LOT of them, and didn't need a large house for 3 people. So we decided to go small, I wanted an actual tiny home with a loft, she wanted an apartment, so we compromised to this older trailer. We dropped our square footage by 57%!! This is the LAST home we will have so we don't mind investing in it even if we spend more than its value, as we just need it to work for our specific needs...

Your 2 x 6 joists 20" apart might not even be code where you are nowadays.
But structurally, you should be OK, because the span is only 12'.
The worst case is a load on the roof splaying the walls outward and putting pressure on the ends of the joists, sending the middle of the floor into an arch. But that's worst case. Heavy walls could do that too, but you would have to find some engineering load tables online to calculate it. I don't think it's worth it.

I would skip the 2 x 6 walls and just put isocyanurate insulation panels (the silver covered foam) in the walls.
It comes in different thicknesses and has an R value of 6 per inch. You could even add just an inch or 3/4" to the fiberglass you have, which probably has an R of 13. 19 would be what you would get with 6" studs.

BUT remember, heat is most interested in going out the roof, second the windows and doors, and walls last.
And with trailers, roofs are often the first thing to go, along with the floor.

I wouldn't even worry about the walls until you are sure about your roof and floor, and happy with the windows being draft free.

Trailers have very short lives in some parts of the country, like Florida, so it matters where it is too.

The insulation is shot, we replaced enough in the bedrooms, so our summer heat doesn't bake us to death... Las Vegas NV heat SUCKS. I don't think it's worth it. The looking up the tables online? The walls would go from 2x3 to 2x4 the only 2x6's are the floor joists at 20 inches on center.Thank You!