(eng): This report contains brief notes on estimation of beta-distributed weight of a Gaussian mixture. The results are directly applied in paper Kárný, M.: On approximate Bayesian recursive estimation]. First, we develop a method to update the beta distribution of weights by new data (evidences) and show, that a projection is needed to preserve the low modelling complexity. Then, we show how forgetting may be applied to improve adaptivity. The results can be immediately applied to multicomponent mixtures.