How much should I weigh?

Well, that depends! A good weight is one that is healthy for you, and where you feel good and are happy with your fitness and appearance.

Ideal body weight is an arbitrary concept, and largely a construct of life insurers more than doctors.

The body mass index you hear about (BMI) is an attempt to use easily available information to factor in your height and not just your weight.

The calculation is:

Weight (pounds)/Height X Height (inches), then times 703.

"Normal" is 18.5- 25
"Overweight" is 25-30.
Underweight is less than 18.5
Obese is 35-40
Morbidly Obese is over 40.

Thing is, this is also somewhat arbitrary. The idea here is an index using height and weight only, since this information can be gotten easily from medical records or even drivers' licenses. It does not include important factors such as muscle mass, body fat content or exercise tolerance.

This article neatly summarizes findings of two years ago that show that the "Overweight" category is actually the healthiest, in terms of lower rates of cancers, heart attacks and strokes.
The Underweights and Obese categories have about equally bad health outcomes. The Obese from certain cancers and heart disease, and the Underweight especially from trauma and infections (or at least poor recovery from them). See this article, too.

Basically, being slightly "overweight" by modern standards may be based more on modern standards of physical appearance than on actual health and well-being. The number on the scale is probably less important within the middle range of body weights than your fitness and activity level.