I like the idea, I think it might make keeping track of your belongings easier. But there is a complication that even visiting places that are not your home can make you take some things out of the bag and add additional ones intentionally. For example, you buy a snack in the cafe and put it in your bag (the increase in weight shouldn't be a problem, but later you eat the snack and the weight goes down again, either you or the smart bag should be keeping track of this). Or you borrow a scarf to your friend whom you met in the city for he/she forgot to take warm clothes, or you drink some water out of the bottle that you carry in the bag while sitting on the bench, the mass of the water that you drank could be equal to the mass of your keys, etc.
The thing is that someone should be keeping track of all these small weight adjustments happening because of various reasons throughout the day, otherwise at some point it will become too complicated to tell whether you lost something or whether the weight changed as a result of your intentional actions. Since the bag won't be able to do this unless it was equipped with additional smart software, the one who would have to remember all that and make sense of it would be the bag owner.
When I leave some public place I was at, I usually check if the most important things are in the bag (phone, wallet, glasses, etc.) I don't have to think whether I drank the water or ate the snack that was in the bag or left something intentionally in the parked car not to carry it around, etc. But if I was using a reminder system that you propose, I'd have to think about these things in order to know whether I lost something or not.