Saying "I want to lose weight" is simply easier to say then "I want to lower my body fat percentage" and though "I want to get fit" is as easy to say as "I want to lose weight," it's a lot more broad. Same goes for saying "I'm on a diet." Saying you're making "a lifestyle change" requires some explanation as to what you mean, where as saying that you're on a diet gets the same idea across, but much faster.
This is the time of year where everyone starts thinking about their weight and physique, because they want to get into their beach bodies. So, yes, I would say during this season, weight is on a lot of people's minds. However, once mid to late summer rolls around, the topic of weight on TV ads and Magazine covers--as well as people's minds--are going to drop substantially.
But again, saying "weight" is easier than saying and having to explain "body fat percentage." Saying "I want to lose weight" gives everybody the general idea of what you want to accomplish (i.e. getting a sexier, and/or healthier body) without causing any confusion.