Only thing lighter weight is an active 4G watch.

My opinion is you need to use a smaller phone. Then a regular looking running waist pouch, arm band, or even a good pocket will work. Look into the small(er) s24, iphone se, iphone normal, pixel, BLU or Tank brand phones.

Rust desk

You like Rev. Horton Heat too?

Too much al-a-bucce-bama for me.

Article posted today has a interesting canidate for you. https://liliputing.com/unihertz-tank-mini-1-is-a-smaller-cheaper-rugged-phone-built-for-the-outdoors/

Let's go HP-VEE