I agree the love story is rather weak.

***do not read any further, if you plan to see the movie soon***

In a way, the love story in the movie became the 'standard' hollywood conventional one that we are use to seeing in movies. Amsterdam was attracted to a very beautiful theiving whore, that has strong ties with Butcher Bill. This makes him very uncofortable around her(who can blame him?).

But the love story plot became soapy Amsterdam heart opened up toward her because she nursed him to back health and offered to share her life's saving with him. In other words, her character turned into the good-girl, help-mate role with the heart of gold. Now she is transformed as the love-able, but theiving girlfriend of Amsterdam.