The phrase "curl one's lip at" means to express disdain or contempt through a facial expression. Antonyms, or opposite meanings, could include expressions of approval or admiration, such as smiling or nodding in agreement. Alternatively, one could also refrain from showing any visible reaction or emotion, maintaining a neutral or indifferent demeanor. By choosing not to curl one's lip at something, one is showing a lack of negative judgment or criticism towards the subject in question. Ultimately, the antonyms for curling one's lip at reflect a more positive and respectful attitude towards others and their actions.