。
I'm not a baby either, you know.
Literal
I [too-だって] baby is-not [strong-emphasis-ぞ].
だって is the casual form of でも/であっても ('even, also, too'). Here attached to 僕 = 'I too, even I.' Expresses the speaker asserting their equivalence with others on some dimension. ぞ is the masculine strong assertive ending. A declaration of self-respect.