The term "weight" has multiple related meanings in both scientific and everyday usage. Even among experts and in textbooks, weight is ambiguously defined as either the gravitational force on an object or operationally as the magnitude of the force an object exerts on a measuring scale. This poses both conceptual and language difficulties for learners, especially for accelerating objects where the scale reading is different from the gravitational force. But while the underlying physical constructs behind the two referents for the term weight (and their relation to each other) are well understood scientifically, it is unclear how the concept of weight should be introduced to students and how the language ambiguities should be dealt with. We investigated treatments of weight in a sample of twenty introductory college physics textbooks, analyzing and coding their content based on the definition adopted, how the distinct constructs were dealt with in various situations, terminologies used, and whether and how language issues were handled. Results indicate that language-related issues, such as different, inconsistent, or ambiguous uses of the terms weight, "apparent weight," and "weightlessness," were prevalent both across and within textbooks. The physics of the related constructs was not always clearly presented, particularly for accelerating bodies such as astronauts in spaceships, and the language issue was rarely addressed. Our analysis of both literature and textbooks leads us to an instructional position which focuses on the physics constructs before introducing the term weight, and which explicitly discusses the associated language issues.