The phrase "have weight" is commonly used to describe something that is significant or important. However, there are several synonyms that can be used to convey a similar meaning. For example, the term "carry weight" suggests that something has influence or authority, while "hold importance" implies that something is valuable or relevant. The phrase "be taken seriously" also conveys a sense of importance or significance. Other synonyms for "have weight" include "matter", "count", "mean something", and "be significant". These synonyms can be used interchangeably depending on the context in which they are used to communicate the desired meaning.