First, that is a sporting shotgun, not a "weapon" as the term usually understood.
Belknap was a hardware distributor and was in business from 1840-1986. (See http://rosetools.bizland.com/id5.html
for information on the company.)
Like other companies in that business, they had shotguns (and sometimes other guns) made and marked with their own name. Several companies, notably Crescent, would do that, but I don't find Belknap on a list of Crescent guns, so some other company may have made those. Some also came from Belgium; the presence of Belgian proof marks will show whether that is the origin of your gun.
Those "trade" guns were usually serviceable enough, but made to a price, and most seen today are plain worn out from being used in a day when carrier pidgeons darkened the sky and there were no game limits. They are not made for modern shotgun shells and should be fired with them. Many have Damascus or built up barrels and should not be fired at all as they could be highly dangerous.
Value depends on condition, but there is almost no collector interest and even in near-new condition they rarely bring over $150. In average shape, they run around $50-75 if one can be sold at all. I strongly recommend you treat it as a wall hanger.