  We answer a question from A. V. Abanin and P. T. Tien about so-called almost
subadditive weight functions in the sense of Braun-Meise-Taylor. Using recent
knowledge of a growth index for functions, crucially appearing in the
ultraholomorphic setting, we are able to show the existence of weights such
that there does not exist an equivalent almost subadditive function and hence
almost subadditive weights are a proper subclass.
