From The Collaborative International Dictionary of English v.0.48:
gaga \gaga\ adj.
1. mentally or physically infirm with age.
Syn: doddering, senile.
[WordNet 1.5]
2. marked by foolish or unreasoning fondness; as, gaga over
his girlfriend.
Syn: crazy about, dotty, enamored, infatuated, in love,
smitten, soft on(predicate), taken with(predicate).
[WordNet 1.5]