grammaticality - Is "We look forward to your spending time with us" a proper use of "your"?

The phrase “We look forward to your spending time with us” is common in invites in my industry but it feels like “all your base are belong to us” to me. :-P

Is it proper English?

Answer

There's nothing grammatically wrong with your in OP's example (but the comparison should be to all your base are belong to us! :). Consider...

We look forward to your arrival

We look forward to you arriving

...where obviously both are fine. In the first case we've got a noun, and in the second it's a gerund. We can substitute spending time with us in either of those roles, so both your and you are grammatically valid. The reason OP often sees your on invitations, etc., is simply that it's rather more formal in tone, and thus seems more appropriate to that context.