[subject] + 毕竟 + [verb phrase]
毕竟 + [clause]
[clause],毕竟 + [clause]
毕竟 brings in a fact that can't be argued with and that explains or excuses something. It goes after the subject or at the start of its clause.
A common shape gives a judgement or a request first, then 毕竟 with the reason behind it.
With 虽然 or 但是, 毕竟 says that whatever the drawbacks, the basic fact still holds.
English "after all" also means a plan changed: "I went after all". That is 最后还是 or 还是. And "finally", after a long wait, is 终于.