Clothing size is definitely more accurate - as previous posters have stated, weight doesn't account for body composition.
As for how much you're 'supposed ' to weigh, if it's based on BMI it's probably bullshit. BMI is an actuarial tool, meant to be applied to entire populations. For individuals, it can be wildly inaccurate, especially if you're not of European descent. Also, BMI ranges were adjusted downwards in 1998, so a fair amount of the obesity epidemic is due to new metrics, not people actually getting bigger.
We're also starting to see in study after study that behaviors like being active and eating well play a much larger role in health than weight. In addition, we're also seeing that weight is often a symptom of underlying medical problems (insulin resistance, thyroid issues, eating disorders etc) and not a disease in itself.
Health is a continuum--no one is perfectly healthy or unhealthy. There is no perfect weight, body composition etc. It's definitely great to set goals for increased fitness and health, especially behavioral goals, but realize that there is no end game. Everything you do moves you closer towards the healthy or unhealthy end of the spectrum. If it makes you feel better in the long run, go for it!
Also seconding the strength training. Not only is it the best way to add muscle mass (and you won't get huge if you're female, you don't make enough testosterone), but it also strengthens your bones and helps prevent osteoporosis.