Pay attention that "fine" in that phrase means "end" (week-end). It does not exist any plural form of "end" in Italian. If for some reason you need to underline the plural, we usually prefer the words "finale" (s.) and "finali (pl.). i.e.: 1) "Hai visto il finale di quella trasmissione?" or 2) "Quel film esiste in due versioni, con due diversi finali." But you shioukld be carefully... "finale" must be used just to define the latest part of a show (or something like this). You can't use it everywhere... What you have read on your dictionary (fini) is the plural of a different "fine" that has different meanings (thin, elegant)

Ciao Vittoria, in questo caso si usa "nei" (nei = in+i) perchè fa riferimento a diversi fine settimana - un fine settimana - due fine settimana. Spero di essere stata utile. Ciao, Claudia