Oh wow .... this is a really tricky situation.

You sound like a very caring person who doesn't want to hurt other people's feelings.

But this is not a two way beneficial friendship (aquaintance). You're not getting out of this it seems like it's more give give give, on an emotional level anyway.

I'd say either ... ignore? Hard, I know otherwise you would have done this already.

Or else you're going to have to start with some random ways to respond when you are invited by thinking of something to do when you're invited the next time. So if your acquaintance says can we do xyz tomorrow (hopefully you're contacted by text) - you can say along the lines, thank you, but no thank you, tomorrow I have to ............

The other option is to give an honest response when you are asked to go out and say no thank you, that really doesn't interest me, I'd rather give that one a miss.

Alternatively suggest somewhere else / something else to do.

I hope that this works out for you!