I play with a thinner pick whenever I need to alot of strumming which involves upstrokes like funk or playing acoustic. But whenever I play any kind of lead playing or power chords, a heavier pick feels better.
That's what they usually recommend. Not much to add

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Lighter picks are better for strumming, IMO. You get a softer sound and you can play quietly without having to try so hard. A heavier pick would give you a lot more string attack, which you don't want when you strum.

Now, for any kind of electric playing, I use a heavy pick simply because if I need a lighter sound, I roll back my volume and turn off the gain. But for acoustics, the general rule is lighter picks are better for strumming.
Nope. Either my Jazz IIIs or my fingers.
Ibanez RG2228 w/ EMG808Xs | Line 6 POD HD500 | Mackie HD1221
Use a pick heavy enough to pick and thin enough to strum. I have that problem too and the Dunlop Tortex 0.96mm solved it.
Dunno how anyone can use Jazz IIIs for strumming, feels horrible. I use tortex 1.14mm (purple) and it suits nicely for the metal i play. Very versatile with good attack
One guy I knew years ago used very thin nylon sheet material for his picks. Almost like stiff paper. Worked great for him...Never played a single note in his life.