그러다 보니 is 그렇다 (right, this situation, like that) + 보다 (to see) + 니 (introducing a consequence clause).
Literally it means 'from what I see' or 'as I see'. In short it can be reduce to 'actually'. The clause that follows this grammatical structure is the consequence from what 그렇다 refers to (usually an observation or something you become aware of).
E.g. 그러고 보니 얼굴이 좀 창백해 보이네요. 오늘 집에 일찍 들어가서 자요. (Actually, you look a bit pale, you should go home early today and rest.)