  A prefix normal word is a binary word whose prefixes contain at least as many
1s as any of its factors of the same length. Introduced by Fici and Lipt\'ak in
2011 the notion of prefix normality is so far only defined for words over the
binary alphabet. In this work we investigate a generalisation for finite words
over arbitrary finite alphabets, namely weighted prefix normality. We prove
that weighted prefix normality is more expressive than binary prefix normality.
Furthermore, we investigate the existence of a weighted prefix normal form
since weighted prefix normality comes with several new peculiarities that did
not already occur in the binary case. We characterise these issues and finally
present a standard technique to obtain a generalised prefix normal form for all
words overarbitrary, finite alphabets.
