I stayed up late, so I'm really sleepy.

Literal

Night-late [obj-を] did-[because-ので], very sleepy-[explanatory-んだ].

~ので reasoning pattern chained with casual ~んだ ending. 眠い is the adjective for 'sleepy.' Note the plain past 夜更かしをした combined with causal ので — a natural two-clause reasoning sentence in conversational Japanese.