Sir John Falstaff is a fictional character that has appeared in three of Shakespeare's plays. He is used largely (no pun intended) for comic relief. He is a companion to Prince Hal in Henry IV, parts 1 and 2, and in Wives Of Windsor.
His character is fairly easy to summarize. He is an obese, vainglorious, cowardly knight. One critic refers to him as a "lying tub of lard." He leads Prince Hal into trouble, and is ultimately repudiated when Hal becomes king.
Falstaff is a fun allusion, partly because his name sounds humorous. Some have argued that it is actually an innuendo for impotence, as if he is so drunk most of the time, he is unable to perform. I'll not say more about that.
I do take requests for Use Your Allusion posts, and my old buddy Jeremy suggested Falstaff might be a good one to mention. Thanks, buddy!
If you ever need to refer to a dishonest, self-centered, overweight person, you might find a way to work in the name "Falstaff."