$300
The model 38 air weight had a steel barrel,but a light weight alloy frame.Smith and Wesson does state what the alloy is comprised of.
Sounds to me that you have a smith and Wesson mod-12.These fine .38 special revolvers are selling for 200-300 dollars depending on the overall condition of the gun.
$20
My serial # is near yours and I purchased it new in 1968.
Informaiton not available in the public domain.
100-450 USD
50-475 usd
Your Smith and Wesson model 37 chiefs special airweight will bring 450 dollars in new unfired condition.It may bring more if the buyer is really motivated.
1982
100-400 USD
100-450 USD
45 years old