Ithaca 37's are nice and light.
It sounds like you want a pump action repeater otherwise I'd suggest a single barrel break action that you could shorten the barrel down to 18"
My previous post about weight was between the Grizzly's...the difference of the 4 inch barrel is minor as most of the weight is in the receiver and stocks.
Personally I'd rather have a full or youth stocked 12.5 then a Pistol gripped 18"er.
Shotgun's are relatively heavy for backpacking there's no getting around it.....you will get used to the weight.
A Mare's leg leveraction in .44mag,.45colt or .357mag equipped with a butstock would be a nice slim relatively light hiking gun.