「持ち帰れないぐらいのお土産を頂いた」
What does ぐらい mean in this case?

質問を翻訳

[Someone] gave me so many gifts that I almost couldn't bring back home. In that case it means like "almost" in English: 死にそうなくらい疲れた。I was almost tired to death. It actually expresses some kind of metaphor, like, in your sentence, the subject seems that he/she actually could bring them back home or somewhere, and in the example sentence I wrote above the subject didn't die of fatigue.