you might want to search some of the photography mailorder places just to see what is on the market. I tend to go to B&H Photo.....
https://www.bhphotovideo.com/

As far as small, lightweight, and inexpensive, I recently bought a Canon Elph 350HS. It was under $200, IIRC. Not as nice as a DSLR, but better than a phone camera. Certainly easier to grab and take a quick shot!

It's not waterproof/resistant, though. Since I can sweat profusely on a hot day, or might get caught in some rain, I just keep it in a ziplock baggie. It's not what you specified, but might be something to consider.


Steve in Peoria