Tom's decision to leave his family is a sign that he is just like his father. He is a weak man who cannot cope with responsibility and finds relief by turning his back on his family and running away. As a character who succumbs to his tragic flaw, Tom is clearly haunted by his decision to leave Laura and his mother behind.
Even though Tom has physically escaped, he tells us in his narrative that he is unable to forget the memory of his sister, that there are many things that remind him of her and he feels very guilty and ashamed for what he did to her.
"Although Tom does eventually assert his independence, he does not seem to ever become fully mature. Rather, he is compared to his father, who also abandoned the family, though he had presumably chosen that responsibility by getting married. It is his father's desertion which places Tom into such an oppressive situation. Because Tom is so clearly compared to his father, readers can easily forget this primary difference between them."
Tom's decision to leave is clearly a sign of weakness because he doesn't even have the guts to tell his mother to her face that he is leaving. He takes the money for the light bill and pays his final payment of dues and decides to sneak out and just not return.
Tom is a coward and a dreamer, he is a man who has no sense of purpose, does not understand responsibility and feels controlled and dominated by his mother. He is dramatic and immature, he is selfish and lacks self-esteem, or he would understand that during a Depression having any job is better than having no job. Tom acts like a petulant child, he runs away because he feels stifled by his mother's personality.
Any decision involving change and breaking ties who are leading you nowhere are, in my opinion, signs of strength and courage. At face value, you could say that Tom was unfair at leaving his sister and his mother behind, while moving forward to a better life. Yet, when you analyze in depth you realize that neither the mother nor the sister were characters of change: They both were stagnant, stale, and stuck within their own demons. Meanwhile, Tom was desperate to get away from the vicious cycle that he continued to see in his home. Would his mother or sister have changed should he had taken them with him? Unlikely. In fact, they may have continued to be an obstacle on the road for him. For that reason, there is nothing weak about realizing one's obstacles for success and happiness, whether they involve embarking on a mission alone, and leaving everyone else (and their choices) behind.