Walt didn't just let Jane die because it was good for his business. He wants Jesse as a partner but also doesn't want him to die. Jesse had been doing drugs on and off for the whole series and you can reasonably label him as an addict. Only now he and Jane were spiraling out of control together and it was just a matter of time before one of them (or both) died.
Walt let her die because she knew who he is and had threatened to reveal it, because Gus' advise "you can never trust a drug addict" was resonating in his mind (therefore she could blackmail him again), because she was just as bad influence on Jesse as he was on her, and because knowing Jesse's drug use history the only way to get him to quit once and for all would be to wake up next to his dead girlfriend and realise not only that he's partly responsible for it but also that next time it could be him.
Walt let her die because she knew who he is and had threatened to reveal it, because Gus' advise "you can never trust a drug addict" was resonating in his mind (therefore she could blackmail him again), because she was just as bad influence on Jesse as he was on her, and because knowing Jesse's drug use history the only way to get him to quit once and for all would be to wake up next to his dead girlfriend and realise not only that he's partly responsible for it but also that next time it could be him.