Limited practical knowledge here (beginner ASL and some time in a linguistics research lab) - there are fewer synonyms, but facial expression and other movements make a huge difference. Much like German adds suffixes that can really change the meanings of words, a eyebrow or tongue movement can modify a sign in ASL.
Another reason ASL has fewer synonyms is that it’s not a horrible amalgamation of a ton of different languages like English is (English has a weirdly large vocabulary, like 3 times as large as some other languages). ASL is a direct descendant of French SL, no weird mixing. Moroccan SL, in contrast, is a descendent/hybrid of several languages and it, as an example, has like a million different handshapes for different kinds of insects.
Further, a word-sentence model is too limited to describe sign languages (I know this applies ASL and Moroccan SL, not sure about others). For example, a large set of concepts are expressed through classifiers. Classifiers are systems of hand-shapes, spatial locations (e.g. side of head vs in front of chest), and motions which can specify a objects (including its shape, size, and location) and also the objects’s verb and relationship with other objects. Some people mistakenly think classifiers are a form of pantomime, but classifier motions and hand shapes have specified and limited meanings (e.g. the flat rectangular object classifier is not making a rectangle shape, it’s more of a pinching motion). That’s just one example of how sign languages diverge from a word-sentence model, many more differences exist.
The main take away is that sign languages work differently from spoken languages, it’s not that easy to compare 1-to-1. There’s definitely no word that means “rotund” in ASL, but there are certainly grammar structures that let you express that.
Although you could, there’s no need to soften or euphemize physical characteristics in American Deaf culture. You can just sign “that fat person over there” and it’s not considered rude.