Actually, Jason ...
... most of the original, commercially produced teardrops of the '40s & '50s were made with 1/2" walls (a couple as light as 3/8", but they had additional framing 'round the doors, windows, and galley wall edges), and no insulation was pretty standard.
I don't think there's anything wrong with 3/4" ply. walls (other that a little weight gain) - they're quite a bit stiffer, and they're only marginally better environmentally.
Depending on which profile/design you choose, I'd recommend no more than 1/4" outer sheathing for the roof (preferrably in two 1/8" layers), 3/4" x 1" to 1-1/2" roof beams on edge (minimum! I use 1" thick by 1-1/2" across ...) doubled at the galley lid hinge and any "seam" of roof/ceiling panels, with 1/8" ceiling sheathing/paneling. Insulation? You betcha ...

...

...!
No doubt you'll be getting lots of other suggestions, but I believe in
KISS: Keep It Strong & Simple! Whatever you decide, Good Luck on your build, and in the meantime ...
CHEERS!
Grant
Celebrating
Retirement after over
32 Years of Building, Promoting, Supporting, Supplying, Living the Lifestyle, and Loving
Teardrop Trailers!"Life Moves a Little Slower When You're On Teardrop Time"The nature of Life, itself, is change ...
"Those who matter, don't mind, and those who mind, don't matter." 