What happened between the 2 weeks and 3 months? Did you contact him?
You say it took him 'over 3 months to finish the job.' Since he 'finished' the job and you did not complain during that time, you likely owe him. Obviously, you made no attempt to stop him from finishing the job--even though it took longer.
It would seem therefore that you owe him. A lawyer will likely cost more than it's worth to haggle. If the work was satisfactorily completed, you owe him.