I am 6'5 never had an issue regarding my medical. Smallest aircraft I could fit in was cessna 152. There is PLENTY of room in cessna 172, I even have to bring the seat forward in that aircraft. The only issue I can think of is appearance. I am tall and sturdy built. Some people get afraid of me when they see me. Thats not a good thing for the passengers.
Although some major airlines like lufthansa has height requirements. Its usually 6'4. But on the other hand if you just planning on working only for major carriers don't waste your money. Its really tuff to get in there.
On smaller airlines I doubt that you will have a problem.