I am 6'2" 280lbs. at the minimum. I look like a football player and wouldn't look out of place on the front line at an NFL game. Big everywhere. Broad shoulders. Long legs. Big waist, nice sized stomach. Tall too.
That being said, I fit on everything fine. My wife (a normal sized 5'5" woman) and I doubled up on everything. I know someone said not to go on Gadget's Coaster above me but I went on it with her in the same car! A little tight, but we were comfortable. Autopia? We both fit in there fine. A little tight, but not squished. Space Mountain? That's always a tight one regardless of being at Disneyland or WDW but I was fine there. Maybe even better at DL since there is the double seat. My wife sat in on that one too.
There is only one ride that might be hit or miss. The Matterhorn, and I can personally vouch that it is tight. I sat on the end. It was fine as far as width wise, but my knees were kissing the back of the other seat. It really came down to having long legs because that was the problem. It was my legs, not my width. They just recently renovated it and I often wonder why they couldn't find a way to alter the seats a bit, but it seems they didn't. Either way, I still fit in there but if I got a leg cramp I was screwed. Despite a rocky ride I didn't get hurt despite being in there tight. So you're 5'9". I don't think you'll have an issue with the length. There is only one way to find out.
Disney is hardly a "bush league" park. They have the foresight to realize Americans are the biggest people in the world. This isn't a Six Flags park or an economy class flight. Their rides accomodate everyone.
