Let me ask you a question. What would you do in this situation:

You meet someone at some group and over the course of a few months you get to know each other and become friends. The group comes to an end and you swap numbers and promise to keep in touch.

A week or so later you message this person. There's no response.

A week later they DO respond, saying "Sorry, life's been busy. Yes lets meet up sometime. What are you doing next week?".

You send a message telling them that you have no plans and are free to meet up if they want to.

There is no response.

Do you message this person again or give up on them?

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See, I'd give it a week or so and message them again. I'd be getting a bit frustrated because I'd feel like I was been messed around and that might show. That's because I've been in this situation so many time that it's getting infuriating.

I'd not be overt about it, just slip it in there such as saying: "Hi, trying to plan my weekend. Been invited to X, but not really that keen. You want to meet up instead at Y?"

Then they go: "Oh my God, you are so needy!"

^ Literally every potential friend for years now.