For 40 years I've heard people go back and forth on this one.
I remember way, way back in the day, a "cool kid" I knew got an Ibanez Roadster. One of the first "modern" electric guitars I ever saw. He did this thing I'd never seen a guitar player do before; he played FAST. It sounded so cool.
He used a thin pick. Said you had to. So, as I was just starting to learn, that was religion to me. Thin picks = fast.
Goes to show how misleading "advice" can be. Years later I came to understand what he had done was "tremolo pick" a heavily distorted guitar, which is something that a thin pick can indeed facilitate. But it's not really alternate picking.
In my formative guitar years, I was a devoted student of the Randy Rhoads school of guitar, and later, Yngwie Malmsteen (and to lesser degrees Tony Iommi, Buck Dharma, Angus Young and Alex Lifeson). I was still very young, but found out that for the most part, the players I gravitated towards preferred heavy picks. Malmsteen claimed it was because "when I move the pick, I want it to do what I want it to do. If it bends, it will not be instant." He was adamant, and of course nobody in the world was delivering what he was, so I simply took it as gospel. Strangely, at the time, many of my guitar playing friends, even the older ones (they being 16) still insisted on thin picks. They just said Yngwie was wrong. Some of the early metal guys were using the thin ones I think, one of the early players from Venom for example.
Over the years, I standardized on heavy picks for the same reason; if the pick flexes, it gets in the way of the extremely fine and precise commands I'm issuing from my brain to my fingers.
But, for some reason on an acoustic guitar, when I strum, I gravitated to medium picks. For some reason a heavy pick (like a purple tortex) just doesn't feel quite right when I play a big dreadnought strummer. Not to mention, the thinner pick creates a different tone when moved across the strings, and I prefer it when banging around some Zeppelin acoustic songs and whatnot.
Light picks, I find them useless. I know there's a reason they exist and I know a lot of people like them, but for me, they do nothing. (I can't stand that in guitar center, if you ask for a pick, they hand you one of the GC branded ones and it's usually lighter-than-medium).
So to me, there is an absolute difference in attack, decay, and overall tone, between picks, and for me, the playable range is towards the heavy side (again, purple tortex is my standard), moving to the green tortex for acoustic if I'm feeling inclined that way at the time.
I know a guy, he's the lead guitar player for a band called Toxik. Grew up one town over from him. He uses very heavy jazz picks, purple tortex weight, but they're short. I don't like them at all (I have a couple of them in my studio). But that's preference. Josh is a guitar player that was way ahead of his time when Toxik was big. Nobody sounded like him, he was an innovator. Maybe one of the reasons for his distinct tone was that he was a heavy metal guy, really a predecessor of progressive thrash, that used a jazz pick.
Something else I found along the way, after experimenting with Herco picks (which Jimmy Page used), Fender picks (which are a kind of slippery plastic), and Tortex picks (and many, many others), the material is also relevant. For me, the Tortex pick is the absolute winner for tone, grip, attack, and feel. So that might be something else to keep in mind.
Lots of options out there, try 'em all. Picks are for the most part cheap, can't hurt to pick up a bag of a variety of weights, sizes and materials (they make metal ones etc) and give 'em all a run. They bring out different characteristics and can even incline you to play differently, which can help you discover something you may not have known about your playing self.