I have been a huge fan of the show, watched all the episodes multiple times and Riker was my childhood hero, but I have never noticed the ridiculous way he sits down. It has been called the Riker maneuver and a Reddit user has a plausible explanation for it:

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

This comment was then replied to by actor Wil Wheaton (Wesley Crusher), who wrote, “Confirmed. Source: I served on the Enterprise with Riker for 5 years.”