It's pretty hard to give a 'right' amount here.
Of course, it's well documented that more content on a page has a strong correlation with improved rankings (and conversions). To say that there is a golden threshold of characters, however, is impossible to say.
I'd rather bring up the point you make about stuffing. That's probably the main thing to keep in mind when writing descriptions or content - don't make it look like you're gaming for a search engine, but keep it great for a user. If you can use your keyword multiple times, that's great. But, as you allude to, writing it for the sake of getting it on the page more often is a bad move.
If 160 words for a description is the absolute most you can say on a topic, without repeating yourself, then 160 is the right amount **in this case. **Other times it might be more, and sometimes it might be even less; it really is dependent on the context.
You might be able to squeeze more content for a description by using things like an example of how a system/process works etc. But I'd always remain focus on writing for a user, not a search engine, and to avoid stuffing where possible, as you rightly pointed out.