I can't give you an exact legit answer, but I also know the phrase putting up and it's very commonly used in canning. I always thought when saying it "putting it up for later" or "putting up in the pantry".

Here in Michigan we often use the phrase "putting up" when referring to canning. Some also say "putting by" and some of the younger canners call it "processing", LOL, but people my age often call it "putting up" food.

Annie

Oh good. It makes sense to me because I look at it this way, you're putting the jars up onto the shelves in the cupboard . . . putting the packages up onto the shelves of the freezer, etc.