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M1 Finance at least lets you set up a portfolio by weight, instead of individual trades: https://www.m1finance.com/

I believe they have an API, so you could automate it.

I think there is a site in the UK called eToro where you can do this. I'm not sure if that's what they do, but it's something along those lines.

Either way, it's a good idea. You might run into regulatory issues but I'm sure it would find a market

Yes, I'm interested. I was thinking along the same lines.