Former friend sounds better.

We often say 'former friend' to refer to someone who used to be our friend. The word 'formerly fat friend' means a friend who used to be fat. We don't usually use 'formerly friend.' Grammatically, 'former' is an adjective, so it modifies the noun, 'friend.' On the other hand, 'formerly' is an adverb, so it modifies the adjective, 'fat.'