I have been searching for the same thing, ideally I'd like to buy an electronic scale with a digital I/O port. You may have more luck finding these in the US than I had in the EU, but in any case I wasn't able to find anything that hooks up to a computer in a non-proprietary way. As with home automation, all products seem to sync to the cloud, most of them in a one-way fashion.

I lost track of this idea a few years ago, so the situation may have changed. But if it hasn't, I see the following options for you:

1) find a cloud-synced scale that offers an SDK or at least some way of retrieving the data from the cloud.

2) buy a low-cost digital scale, take it apart and see what you can do with a voltmeter and a soldering iron. At the very least, you should be able to hook into the raw analog weight data which you could feed to a Pi with an A/D board. The nicer solution would be to siphon off the digital value. Even in scales where one chip does everything you could still try to pick up data going to the LCD. However, that might require some epic cabling and soldering, not sure it's worth it.

3) cheesing it: hook up a networked camera and point it to the scale's display. You can do this with any old android phone and a remote webcam app. Have the software on the Pi (or some other computer) pull the image when you step on the scale, run OCR on it, write the value out to wherever you want.