One week its an "Alignment" meeting between me and my manager. This is a time where the manager can talk to me about my current tasks and if I need any assistance from him. We also go over our yearly goals on a regular basis here, just so we can make sure that I am on the right track.
The next week we have our 1:1 meeting. These are lead by me and gives me dedicated time to discuss anything I would like.
What I described above is the only structure to the meetings. If manager doesn't have much to discuss in our alignment meetings he opens the floor for any 1:1 type of discussion and on the flip side, if I wanted to talk about my current blockers during my 1:1 meeting that is also fine.
So to answer your question, our 1:1 are biweekly.
One of my previous managers would just drop by my office on Friday afternoon to check in. This was shorter and shallower, more of a status update. My 1:1s tend to have a longer term focus: handing off responsibility for a project, and discussing which upcoming projects sound interesting.
As a soon-to-be manager myself, I will probably start with weekly 1:1s until I get to know the team well enough, then drop back to biweekly.
A couple years ago, I asked him to meet weekly and he obliged. It felt like he wasn't willing to actually engage in the discussion. I walked back that request to two weeks and then monthly.
I've been trying to talk less as well, since I realize that it's a one-sided conversation. It's difficult for me though, since I feel like we should be talking more.
i would say every other week should be perfect.