These days babbitt spoons are mostly of historical interest, but for many years a lot of machinery used babbitt bearings. They were cheap and could be made on the spot. Babbitt was reportedly invented in 1837 and was a popular material for bearings thereafter. It comes in a variety of mixtures, but is usually some combination of Tin, Lead and copper. It was used widely until the 1930's. The classic poured babbitt bearing could support massive loads at low speeds, and alas these spoons are for pouring babbitt bearings. Logging and sawmill machinery predating the 1930's frequently used babbitt. In more recent years the quest for lighter weights and higher RPM's has fostered a move to roller bearings.
The smaller of the spoons has a special handle on it. The handle labeled "Powell Mfg Co., Appleton, Wisconsin", is a bit unique. The hand grip is a piece of cast iron which slides the length of the handle. Presumably it can be moved away from the heat source while the babbitt is being heated up and then slid down near the spoon to facilitate carrying the spoon from the forge or other heat source to the place where the pour is to be made.