Thinner ukuleles tend to be louder and more lively sounding, and have more sustain, but all of this is really hard to generalize. Different builders use different techniques, bracing, glue, etc. Wood matters, strings matter. It all impacts the sound, and you can't necessarily tell by looking at it or weighing it.
I don't feel that ukulele design is at the peak, things always evolve as builders try new things and people ask for different features. For example, radiused fretboards or side ports are fairly new, and no doubt in the future other innovations will be introduced. Preferences are a big thing, not just sound, but also playability, and there are few rules of thumb. (This is part of the reason why many of us have multiple ukes, even high-end ones).
Are you living reasonably close to the Southern Ukulele Store? Visiting them and trying out different instruments may be the best course of action if you want to get it right in the first try. I just sent back a €1750 uke even though all the specs were right and it sounded fantastic, but it wasn't the right uke for me and my situation (instruments I already have, what sound I want, etc). By objective standards, it is and was great, no doubt perfect for many folks, just not for me. But specs can't tell you whether it's for you, and that is the biggest challenge of buying an expensive instrument unseen (untouched and unheard).