。
She has a real weakness for sweets.
Literal
She [topic-は] sweet things [target-には] eyes [subject-が]-not.
甘いもの literally 'sweet things' covers the broad category — cake, candy, dessert, anything sugary. には stacks the target-marker に with the contrastive は: '*as for* sweets [in particular]' — singling out this category against other things she might *not* be weak for. 目がない as an idiom literally says 'no eye exists,' figuratively 'one has weakness for / can't say no to': the eye, which would normally exercise critical judgment, simply isn't there for this category. Same idiom appears across many languages in different metaphors — Japanese reaches for sight, English for the heart ('have a heart for') or stomach ('weakness for').