精々【せいぜい】

精々 means "at most", "at best": it puts a ceiling on an amount or an outcome, and the speaker thinks the ceiling is low. It goes before a number, an amount, or a verb followed by くらい. It is usually written in hiragana, せいぜい.

With an outcome rather than a number, it is "at best": even if all goes well, the result is modest.

精々 or 多くても

おおくて多くても and さいだい最大で give a neutral upper limit. 精々 adds the speaker's view that the amount is small or the result unimpressive.

精々頑張って

With a request or an encouragement, 精々 means "as much as you can". せいぜいがんばって頑張って can be sincere, but it often sounds sarcastic or condescending: "go on, do your best, for all the good it'll do". When you mean it, say がんばって頑張って without 精々.