Mostly, I refuse and explain why I am refusing. I write replies like:-
"I have nothing to contribute to this, so I see no value in attending this meeting."
"I see that point 3 on the agenda is relevant to me, can you bring me into the meeting at that point"?
These are professional answers. You are telling whoever has invited you that you think your time is better spent, on behalf of the company, doing something else. If they then insist despite your protests, you have to accept it. Although you might at some point realise that the person you are working for is an idiot.
There's a place for meetings, but if you're efficient, they should be rare, small and short.
No, you don't need a weekly project update meeting. I can send you something out of Jira and if there is an issue, you can post a reply to it, or email me. And I can spend time thinking about what you've written and write a careful reply. Only when that still doesn't work, do we do a synchronous meeting, at which point we cover only the points of contention, and with as few people as necessary.
The other beauty of tools like Jira is that the conversation is preserved. Why did we approach the problem that way? Well, go look at it. You'll have someone asking why we can't do a thing and a reply pointing out the problems of that and hence why we have to do it this way. You don't get all of that from the email of the meeting.
"I have nothing to contribute to this, so I see no value in attending this meeting."
"I see that point 3 on the agenda is relevant to me, can you bring me into the meeting at that point"?
These are professional answers. You are telling whoever has invited you that you think your time is better spent, on behalf of the company, doing something else. If they then insist despite your protests, you have to accept it. Although you might at some point realise that the person you are working for is an idiot.