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You’re a little confused, and it’s tricky. Beta is not used to calculate the weight of the stock in the active portfolio, beta in this context refers to the Beta of the active portfolio as a whole.
TB model assumes that you have found a collection of securities that are expected to have alpha. If you take all of these securities and put them into a portfolio, you have the “active portfolio”. The weight of these securities in this portfolio will be determined through mean variance and risk appetite. Once you have this established, you need to determine the Beta and SD of this portfolio as a whole in order to  determine the optimal weight of the portfolio.
Why do you need the Beta to determine the weight? Because you need to know the exposure to the systematic risk. If the portfolio has a high beta, all else being equal, you want to hold more of it relative to the market portfolio