Allegedly a back injury is behind the maneuver. From a post on Reddit and confirmed by Wil Wheaton. Scroll down the Reddit post to find the section pasted below. The reply from user 'wil' is Mr. Wheaton.
[–]AmishAvenger 1162 points 2 days ago*
Frakes had a back injury, caused by having a job moving furniture. The result is the "Riker Lean," where you often see him on set leaning on chairs or consoles, or with one leg propped up on something. You can also see his body is tilted a little when he's standing up straight.
I'd guess this has something to do with that. For each time we see him sit down, he probably had to do that same move dozens of times for each take. Just lifting one leg and sitting right down was probably easier for him than turning, contorting his back, and squatting down over and over. It's the same thing with the Riker Lean: he probably had no problem standing up for a few minutes, but shooting that show probably resulted in standing on set for hours on end. Dude had to find a way to work around his injury by leaning on things, or he wouldn't have made it.
EDIT: Apparently my highest-rated comment is about Jonathan Frakes' back injury, and how it affected his time on the set of TNG. Could be worse, I suppose...
[–]wil 906 points 1 day ago
Source: I served on the Enterprise with Riker for 5 years.