Biff steals things because it is his passive-aggressive way of getting back at people he feels have unfairly done better in life than he has, but also because stealing gives him an excuse to quit whatever dead-end job he happens to be in at the moment.
Consider Act 1, in which Biff and Happy are speaking alone.
Biff: Well, I spent six or seven years after high school trying to work myself up. Shipping clerk, salesman, business of one kind or another. And it's a measly manner of existence...And always you have to get ahead of the next fella. And still -- that's how you build a future.
A little later in the scene, Biff wonders about a former employer: "I wonder if Oliver still think I stole that carton of basketballs." Happy consoles, "Oh, he probably forgot that long ago. Anyway, he didn't really fire you." But Biff replies, "Well, I think he was going to. I think that's why I quit."
This pattern of subtle revenge and avoiding of mundane responsibility is exposed to be a nearly life-long pattern for Biff, and one that will continue.
Biff steals things because he is a kleptomaniac. He essentially cannot help himself when he steals Bill Oliver's fountain pen and runs out of the room. Willy has raised Biff to be a selfish, superficial individual with very little moral values. Biff has been stealing various items ever since he was a child. Biff has stolen basketballs, footballs, building materials, and even a suit. When Biff was an adolescent, his father even encouraged his bad habit. Willy raised his children to believe that the most important thing in life was to be well liked. As a result, Biff has no moral compass in his life and has never been told anything different. He was also never taught the value of hard work. Instead, Biff tries to cheat his way to becoming a success. Stealing is often an easy way to get what one wants, but is not the right thing to do and is illegal.