-(이)라 가지고 is the spoken stand-in for -(이)라서, 'because it is': 둘 다 부산 사람이라가지고 (because they're both from Busan), 태어나서 처음이라가지고 (because it was my first time ever). The 가지고 part adds nothing to the meaning — it is filler that softens the sentence and lets the speaker trail on. Every line here is a noun plus 이라가지고 giving a reason, and it belongs to speech, not writing.