We go on dates every weekend.

Literal

We [topic-は] weekend [of-の] every-time date [object-を] do.

のたびに ('every time, each time') is a fixed temporal expression — の is needed with nouns to make 'on every occasion of [noun].' 週末のたびに = 'on every weekend.' デートをする ('to go on a date') is a light-verb construction using the English loanword デート.