A "loud sigh" means she thinks you are an idiot at that moment, and wonders why she is wasting her time standing here arguing with you over "Nothing".

一声“大声叹息”意味着她认为那一刻的你是一个白痴，而且不明白自己为什么浪费了这么多时间站在这里来跟你争论“无关紧要的事”。