It is an adverb and it means "at the most". It is used when you mention the maximum capability/possibility of something with a generous estimate. It is sometimes used in an ironic way.
I’m broke because I bought a new car. I can't spend more than 50 dollars for fun this month.
新車を買ったから金欠だ。今月は趣味にせいぜい50ドルしか使えない。
新車を買ったから金欠だ。今月は趣味にせいぜい50ドルしか使えない。
Meg and Amy are catching up.
- Meg : I’ve gained some weight lately. I haven't been able to work out at the gym due to the COVID-19 pandemic.
最近太っちゃった。コロナのせいで、ジムで運動できないんだよね。 - Amy : Same here. The most I do is take walks around the neighborhood.
私も。せいぜい近所を散歩するくらいだよ。
Meg and her boyfriend are talking about their vacation.
- Tom : Honey, how many days off can you take? How's work looking?
メグ、何日くらい休めるの？仕事はどんな感じ？ - Meg : I think that the work I'm doing now, can be done in about 2 months tops. However, I can only take around a week off because I have to start a new project.
今やっている仕事は、せいぜい二ヵ月で終わるよ。でも、新しいプロジェクトが始まるから、せいぜい一週間しか休めない。
Ken and Leo are talking about the upcoming game event.
- Ken : Do you want to go to the event with me? It seems that the tickets are going to be sold out.
一緒にイベントに行く？チケットが売り切れそうだって。 - Leo : Yeah, I'd love to. I think that he was a second-rate player at best, but he has gotten better now.
うん、行きたい。(例の選手は)せいぜい二流のゲームプレイヤーだったのに、今は上手くなっているよね。 - Ken : I'm so excited. I guess that the event room is small and only thirty people will find a seat at the most.
楽しみだな。たしか、会場は狭いから、せいぜい30人しか座れないはず。 - Leo : We should go there early and get good seats.
早めに行って、良い席をとろうよ。