I had a leaky tire, so I took it in to be checked for a puncture. The guy found no puncture but found it was leaking air where this clip met the tire:
That clip had been there since I bought the car, I never really paid it any heed. The tire guy had limited English, he got across that he strongly thought I should remove it and that it was causing the leak, but couldn't explain why it was there in the first place.
To show what they look like before removal, there's what looks like one more still on a non-leaky wheel, but it's a bit smaller:
Some image search suggests these might be called "Metal Clip Tire Rim Wheel Balance Weights" but I can't find a good explanation of what they're for, or how I'd go about figuring out if I need them, which wheels need them where, etc.
I've removed it, and the tire seems to no longer leak, but I don't like removing things without understanding why they might have been there in the first place! What's the benefit of adding these to a wheel?