OP
Do you think it would be worth having a conversation with him about it?
Even though you say he doesn’t always be so tight, the few times he has done it has bothered you, and I don’t think it will stop bothering you.
You can’t really know until you know his motivations really?
Was he short of money those occasions?
Making you pay for to stuff on your birthday is weird and not really on. Obsessively sharing costs of meals with a partner is also weird.
In my mind, if he has money to spare, this is the behaviour of someone who doesn’t value you enough.
Or perhaps, if he has money, maybe he wants to save.
Raise it and see what he says?
But realise that it might be he is tight and consider whether it is an issue you would be able to live with? I can’t imagine money issues getting easier if you moved in together and you have children from other partners in the mix too.