I assume they'll handle it the same way Amazon Prime Now seems to handle delivery from Whole Foods: it's a platform where weight doesn't actually matter.
I get insanely variable results when I have Whole Foods items delivered via Amazon Prime. 2 lbs of chicken breast might be as little as 1.2 lbs, or as much as 2.5 lbs. In either case, it's priced as 2.0 lbs. If you're savvy enough to weigh it and realize you've been stiffed, Amazon refunds the entire item, so it's a win for the consumer...I guess?
In general I find that my weight-based fruit/vegetable/meat/bulk bin item purchases via Prime Now slightly exceed whatever I actually requested and paid for, and Amazon never charges for delivering more than you initially requested. But maybe 1/8th of weight-based items will be drastically under-weight. I have a kitchen scale handy, so I always catch this and report it. Amazon has never failed to refund the full cost of the item, but I do wonder how many other consumers are never noticing that they've been scammed when Prime Now fails to deliver the weight that was paid for.
Another huge regional grocer, HEB, does this in Texas with their largest and most upscale stores, and it's been a norm for nearly a decade.
Alternatively, the entire shelf is a scale, but the shelves are smaller so that only one person can pick vegetables at a time.
This would run afoul of commerce laws in pretty much every US state. Tare must be set from zero, not relative to whatever happens to be on the scale, and certainly not on the fly.
Another approach would be to have a scale and require them to stick their potatoes on it, but not require the other, tedious steps like entering a PLU code or printing a sticker. If you can track them picking up items off a shelf and putting them in their cart, presumably you can also track an additional intermediate step where they put it on a scale. (And connect that scale to the network, take a reading when you see them stick potatoes on it, and correlate that.)
Of course you can always just sell by unit and not in bulk. Sell 1 pound, 2 pound, and 5 pound, and 10 pound bags of potatoes instead. Maybe even 0.5 pound if someone wants a small quantity. Or for things whose size doesn't vary much (like apples), just sell by number of apples.
For steak, the packages are normally already weighed and labeled, so the problem might be easier if you can just scan a label that's already printed.