You should define 'lightweight.' A .357 that weighs ~25 oz is pretty light weight for that cartridge.
Here's a few .357's that weight less than 20 oz.
S&W 340
340PD
360, not fixed sight, but does have a 3" bbl.
Ruger doesn't really make anything like an Airweight. Taurus has several .38 revolver models less than 20 oz.
I have a J frame .357 M640, and even with .38's, I'm no good with it. I opted for a K frame .38 3" bbl instead. The recoil with .357's makes the revo useless to me after the first shot. I've considered using a M36 with .38's, but even then I think I'd have to go to combat grips instead of boot grips to hit anything past five feet. I can't imagine firing .357 out of one of the airweight scandium revolvers than S&W manufactures. I think it would be like holding a stun grenade. I'd be interested in something like a J frame M36 w/3" bbl.
I'll tell you something else that's been interesting me lately, and that's revolvers chambered for .32 H&R Magnum. There aren't too many, but the ones that are out there usually go for ~$400.
S&W 432PD
Ruger SP101
Taurus 731, but it's ported
Ballistics almost reach .38 Special levels, but with (purportedly) less recoil.
Also possible would be .32 S&W Long, but only as a BUG. The ballistics for that cartridge aren't much worse than .32 ACP. Slower bullet, but heavier. S&W made a M30 & M31 in that caliber and they occasionally show up used on gunbroker.com and the like.
jmm