First he stole our bin bag (black bag the council says we need to use now or bin will not be collected.) It even says our flat number on it!
Last week, I got the bin bag back, after collection and gave it to DH in the hall on way to school run. The neighbour then got it back off DH saying it was his!
He has also been asking for more and more favours. First DH helped him and his son, move a piece of furniture from his flat. Since then, he keeps bumping into me and saying "Is DH around" as if he just is sitting waiting at home to do jobs for him. I explain he is working / busy and he needs to speak to him if he wants something. It's usually plumbing or odd jobs.
We do already do quite a bit for our neighbours such as pay a weekly cleaner for the shared hall (and ask for money at end of year) and other things such as arranging servicing of the communal fire alarm which involves notifying and arranging access to the other flats.
It is not a question of cost, this is the neighbours second home, and I feel this is a but much.
It came to a head last night, because as he hasn't got in touch with DH the neighbour has not started ringing out flat buzzer at around 9pm (so just after DC gone to bed) trying to get hold if him that way!
We actually hid yesterday. 
but both is us are quite cross. Neighbour has a son but he told us he 'could not cope with the children' when they were young and left. So, maybe not much support there, but anyway that is not really our business.
AIBU to think he could just get a handyman / plumber, and we are not some kind of housekeepers? I am avoiding him now but know he will soon pop up and say "Is DH around" in fact think he waits and pops out at times.
Oh, with the bin bag, I have already contacted the council to ask for more including one with his flat on, so that might help, when it arrives. It is just the other requests. DH is now saying he wants to move because of this. 