Walter is probably a 7. While his ambitions to "be somebody," to become more than his father was, to make something of himself has a 3-ish flavor, it can't be pinned to just 3-ness. 3s don't have a monopoly on ambition, and Walter wants to transcend the racial and socio-economic situation that he and the rest of the black community finds themselves in. Walter hears white boys he chauffeurs talking about investments all day long and a friend of his even started a dry cleaning business that grosses $100k per year. He wants out of his circumstance and he is willing to make a reckless bet on what seems like his only chance.
Walter is uninhibited in his expressiveness and lights up the room when he is having fun, like when he dances with his wife. He can be quite demanding and unselfconscious in his temper tantrums, like a 7 and unlike a 3. Walter seems to be a 7 a the end of his rope... he's lost the capacity for sunshine and becomes childish, dismissive, and hurtful in the style of a 7. "Who cares about you anyway." He escapes to drinking, makes no attempt to hide his foibles, and even skips out on work without calling in (unlike a 3).
The 7→5 security point (where 7s become cynical, provocative, and dark) is clear throughout the movie, but especially in his final breakdown when he is ready to sell back the house.
(Btw, Walter and Mama's misunderstanding can also be understood through a lens of Spiral Dynamics... Mama, coming from Blue, with a childhood memory of segregation and even more profound inequality, is a "stay the course," be faithful, work hard, and make your way slowly into the sunlight kind of a lens. Walter, the product of 5 generations of Blue, find himself with more potential for economic success than any of his ancestors, yet is held frustratingly held back by circumstance. In his job as a chauffeur, he finds not dignity and the promise of a better future for his child, but a trap, a ceiling that artificially constrains his success. He is inhabiting an Orange mentality but living in a world still operating in a racist and socio-economically entrenched Blue paradigm that hadn't yet given way to Orange opportunity for all.)