게 배다

soak in; become second nature

배다 is something soaking in and staying there — seasoning into food, a habit into the body: 간이 진짜 고르게 배었네 'the seasoning has soaked in evenly', 몸에 배어 버린 발성 'a way of projecting that has become second nature'. The point is that it got there gradually and cannot easily be removed: 나도 모르게 배어 있는 거잖아. Careful — several lines here are not this verb at all but the noun 배 'belly', as in 배 나왔어요.