The general physics behind is that heavier gauge strings are thicker, so there's more metal (ie larger coil) moving in the magnetic field of the pickups. This induces a more powerful electrical current, in effect a stronger signal. Stronger signal = fatter tone.
It works for me, but I don't think it always applies. Using thicker strings would make it harder to get a super clean sound while playing lightly, if the amp is cranked up quite high. You'd have to be REALLY light with your touch, or roll the guitar's volume to almost nil so the amp doesn't clip.
Billy Gibbons was mentioned above- it's been said that on some albums, that he'd crank the gain right up, set the tone controls quite low, and then play really lightly on the light gauge strings. I guess for him this produced his famed gritty "dirty clean" sound that gets a lot of raunch when he hits the strings a bit harder. I personally love his old sounds like on La Grange, as well as the processed sounds on Eliminator.
I'm guessing that Stevie Ray went the other way- he'd set his amps quite clean (did he? As I said I'm only guessing! But he did have some Fender amps in there that didn't have much gain), and then use thicker gauge strings. The thicker strings would produce a fatter sound that would overdrive the amp if he really dug into them, but his signal stayed quite clean if he played softer, as well as the amps not being set for much dirt.
Anyway both musicians had a lot of expression in their dynamics which I appreciate more than any of the shredders out there.