How much weight does one have to lose to improve their general health, is there a rule of thumb about that?

Not much! Surprisingly, you don't have to lose much weight to gain health benefits such as lower blood pressure, lower cholesterol, lower glucose (sugar) & lower mortality. Assuming that someone is overweight (body mass index 25-29.9kg/m2) or obese (>=30kg/m2), they can notice benefit by losing just 10% of their current weight. In other words, it's not necessary to lose 50-100# or more. So get started!
Weight loss. This question can not be answered without knowing at what is the starting weight and height and bmi is.After knowing that you need to know if there are other risk factors, and then you can reach what the ideal or shal i say desirable weight should be.