"Because it's me." 나라서 기다렸지... (I have) waited, because it was me... Other people (less nice) would have gone.

나라서 in 한없이 약해 빠진 나라서 means something like "because I am that way". It's a bit involved grammatically. - 나라서 = 나여서 = 나이어서 = 나(이)다 (= is (이다) me (I)) + -어서 (because). 한없이 약해 빠진 modifies 나(I, me) like a relative clause. So it like "I who am/is hopelessly/utterly weak", although it's an uncommon construct in English. Perhaps you can say "I, someone who is hopelessly/exceedingly (한없이) weak". In Korean such constructs are very common in song lyrics. E.g. [아무것도 없는] 나 = I [who have nothing]. [잊혀져 버린] 나 = I [who have been forgotten (by you/others)].

You should put the whole sentence or at least the part surrounding the word. 나라서 is not a single word but a conjugated form which can be interpreted as 나 (I) + 라서 or 나라(country) + (에)서.