"서로 탓 따져봤자 문제는 항상 주위를 겉돌아" => Even if we argue who's to blame, the issue just keeps spinning wheels. (Blaming each other will not bring the problem to resolution.) 서로 따져 봤자 = 서로(mutually) 탓(fault, blame) 따져(argue, debate) 봤자(even if we do ...) -(아/어) 봤자 (보았자): even if you do something (usually followed by a negative). 봐야 and 봐도 are similar. "엎질러진 우유 놓고 울어 봤자[봐야] 소용없다": It's no use crying over spilt milk. (= 엎질러진 물이다) "밑져 봤자[봐야] 본전이다": You have nothing to lose (literally "The loss taken is actually back to even"). 문제는 항상 주위를 겉돌아 = 문제는(the problem) 항상(always) 주위를(the periphery) 겉돌아(circle in futility). - 겉돌다: circle the perimeter in futility. Beat around the bush. Spin wheels without making progress. (겉 = surface, outer layer. 겉+돌다 = circle around on the outside = waste effort without getting to the crux)

봤자 is used to express a hypothetical scenario. -았 may look like a past tense construct to you but it has nothing to do with time information at all. It is similar to a mood indication (imagining versus indicative - actually happening). Suppose we keep poking at each other's fault - approximates the english way of saying the same thing. C'est assez similaire à la phrase suivante: Mettons que nous nous acharnions de nous chercher les petites bêtes...