Re: Devil's advocate says...
Judging by the interior of our fridge after Herself has emptied our local Tescos, having weighing shelves wouldn't work. It tends to get so much stuff in there, often stacked up, that it looks like a chilled but edible variant of Tetris.
Plus if you can only put stuff on allocated spaces inside the thing, then it'll also need standardisation of packaging shapes/materials (for uniform weight from brand to brand) which is a whole other ballgame.
There is of course the slightly easier options of a "to buy" list stuck on the door of the thing that gets filled in as things are used up (or getting close to being used up) which then becomes part of the shopping list, or of course just looking in the damn thing and quickly inventorying it before going shopping.
But of course neither of them are innovative, sexy or high-tech (unless you stick a tablet onto the door to act as the list), they just quietly work (most of the time)...