The 1940 Ithaca Gun Co. catalog says about 6 3/4 pound for the solid rib 12-gauge --

[Linked Image from i.imgur.com]

while for the plain barrel 12-gauge they say "may be had as light as 6 1/2 pounds."

I don't know about Ithaca Model 37s, but I have a 12-gauge Remington Model 31L with a 30-inch solid rib barrel, that is very muzzle heavy. I think it would be much better balance with a 26-inch plain barrel.