I wrote this sentence and I would like to know whether the word "cleverly" is positive, negative (like e.g. cunningly) or neutral.
Lose weight cleverly in the privacy and comfort of your home!
Clever can have positive or negative overtones, but, more often than not, it's regarded as a positive term. (One exception is in the realm of writing software, where cleverness is not considered a virtue.)
That said, I don't think I have ever seen the word used in association with weight loss, and I wouldn't recommend it in your sentence. If you're trying to emphasize the practicality of home workouts, I think smart would be much better:
Lose weight smartly in the privacy and comfort of your home!
And I think it could be improved even more if you didn't use an adverb:
Be smart and lose weight in the privacy and comfort of your home!
It's hard for me to explain why smart or sensible would be better than clever. The dictionary definition seems to fit just fine, but cleverness implies a certain level of genious that makes it seem like a bad fit for weight loss, unless maybe the rest of your paragraph delves into creative ways to exercise by turning parts of an ordinary home (such as stairs, doors, and furniture) into a home gym. To be smart is to be pragmatic, to be clever is to be surprisingly ingenious, and think of something that other people aren't likely to think of. In the case of losing weight at home, that sounds like an exaggeration.
To be "clever" is generally seen as a positive thing. It could be negative in context. Like if you said, "He cleverly avoided doing his job so others had to do his work for him", or "The murderer found a clever way to kill his victim without ever being suspected", I'd take that as pretty negative.
As JR says, the wording of your sentence would strike most fluent English speakers as odd. We generally don't think of a weight-loss plan as "clever". It might make sense in context, though, if you explained it. Like, "Here's a clever way to lose weight ... blah blah details blah blah ... You don't have to exercise or give up the foods you love, just ... blah blah ..."