Can I increase the centre bore on some rims I just bought?

My rims have a 67.1 mm centre bore. I bought some winter tires on rims with 64.1 mm centre bore. Otherwise they fit fine. I was going to take them in and get them changed from their rims onto my rims, but 3 mm isn’t a heck of a lot.

Could I just use an angle grinder and bore out the centre by an additional 1.5 mm on the inside hole? Is that easily done or am I in for a nightmare and a substantially weakened rim?

There’s no way you can do that by hand and expect it to work!
You will never be able to stay centered.
The only practical way would be to use a lathe or a circular indexing table on a milling machine, and that would surly cost more than it’s worth.

Not to mention weakening the rim itself.

plus, even with acorn lug nuts there’s no guarantee the wheels will be centered properly.

The center bore is what centers the wheel, not the lugs or bolts. Never, ever try to drill out a center bore.

A wheel shop might be able to, using a special lathe or drill press.

There’s definitely nothing wrong with having a machine shop do this, but between the costs of the actual boring and having the tires unmounted and remounted it may just be easier to get a set of cheap rims. They may also look at you like you’re crazy if you’re in an area where the whole rims thing isn’t a thing, but there’s no reason why they shouldn’t be able to do it.

I think if you were really methodical about it, you could probably pull it off yourself. If you do some googling you’ll see various creative suggestions for doing it at home. (Using a hole saw and measuring with a board seems to be a common one.) It’s not really a safety issue in that shaving a couple millimeters off the center isn’t going to significantly weaken the wheels or make them fall off, just if you wind up with an oval instead of a circle you’ll get some pretty horrific vibration.

You also might be able to get a small adapter plate/spacer that goes between the hub and the rim that’ll make it work. It might look a little silly though.