Airweight was the name S & W gave to their early aluminum alloy frame handguns. I believe that they were all built on their "J" frame, hence the J prefix. If your handgun has an exposed hammer it is a Model 37 Chief Special Airweight, if the hammer is covered by a shroud it is a Model 38 Bodyguard Airweight. I believe that the model # should be visable by opening the the cylinder and looking at the point where the cylinder yoke indexes when the when closed.
Up unitl @ 1957 model numbers were not used. Check inside the frame near the crane, it has a model number, it will be there.
Impossible to answer without a detailed description of all features, condition, finish, accessories, etc..
$20
Informaiton not available in the public domain.
There is a problem with your question. The Model 36 is a standard weight J frame. The Airweight verison was a Model 37. J frame serial numbers were all numbers until 1969. The serial number you list is for a fixed sight K frame made in the 1961-1962 time frame. That would be a Model 12 Military and Police Airweight.
50-475 usd
100-450 USD
1982
45 years old
100-400 USD
100-450 USD