Great idea! Although we would say that, as our studio has been exploring a similar concept over the last couple of months, albeit from a food waste perspective. :) Some points to add that have come up in our early brainstorms. We don't have answers to all of them!
We totally agree that (as with all the best Quantified Self products) usage should be as frictionless as possible. You need the initial behaviour change to be as small as possible to encourage take up.
What's better? A device that sits in the bin or a device that you use on the way to disposal? Technically, the latter might be easier to build as it's a one-hit weigh & submit. A device in the bin might need to recognise when you're removing a full bag of recycling and take a weight reading at that time. It's not insurmountable, but it's 'a thing'.
The competitive element is a great motivator on many levels, from neighbourhood, to town and upwards. You might want to consider that different local authorities collect different forms of waste in different ways, i.e., different local authorities recycle different things. How do you best create a level playing field between different places?
Is creating recycling necessarily a good thing or a bad thing? How do you reward the household who re-use their waste, or choose to buy products with less packaging in the first place? A really valuable metric would be recycling relative to purchases. i.e. a household's 'inflows' against its 'outflows'. Is there any scope for measuring that?
Really looking forward to seeing where you go with this!