I suggest you change your thinking
There is no way to just lose fat and not lose weight. You could diet and do cardio to get rid of your extra belly fat, but that will leave you weighing less. So you have two options:
1) Decide you don't care what your weight "should" be. Charts that tell you what your weight should be based on your height are based on averages. There are always going to be some people who are heavier and perfectly healthy/fit, and some people who are lighter and are perfectly healthy/fit. For a woman, how curvy you are plays a big role in where you fall in the healthy weight range curve, and for everyone your bone structure also has a big influence. If you are naturally a small-boned person - narrow shoulders and hips, etc, you are going to be on the lighter side of the healthy range even when you are fit and lean. Rarely is it a great idea to GAIN weight just for the sake of weighing more. If your doctor says you need to gain or you are having healthy problems or just feel weak and/or frail b/c of your light weight--then gaining may be a smart move. But don't let some chart tell you how to feel about your weight. You can diet and do cardio to lose your stomach, you'll weigh a little less--but maybe that's ok. More detail on what cardio to do below.
2) Watch what you eat, do some cardio, and do strength/resistance training. This combination will allow you to burn off the fat on your stomach and ALSO gain muscle - which since you don't have a lot of fat to lose should result in a small net gain in weight.
I do not think you should do a lot of ab work until after you start losing the belly fat. If you do a lot of ab work the muscles there will thicken and can actually make you look MORE fat b/c the fat on top of the muscle will protrude even more. Core work that uses your back, obliques, and mid-abs together is fine (planks, jacknives, reverse crunches, ab rollouts), but avoid exercises that isolate one section of abs (crunches, situps, ab machines).
I do not think you should worry about looking like a body builder. Never in the history of humanity has a person woken up one morning after weight lifting looking like a body builder. Acheiving the body builder look is a very very long, slow, intentional, grueling process - and it's extremely hard for small-boned people to acheive. It's never something that happens by accident. If you don't train like a body builder, you won't look like one. And chances are, even if you do, you may not!! Body builders do a lot of isolation training to completely fatique a muscle in order to make it grow in relation to the muscles around it to acheive a certain look. People who weight train simply to get lean, be healthy, and look fit (toned, defined) typically do a lot of full-body training using exercises that utilize multiple muscle groups - combo moves.
You don't get to choose where your body puts on or takes off fat from. You can't spot train your mid-section to get rid of belly fat. The only way to do it is to stay on top of your diet (eat slightly below your caloric demand, drink lots of water, eat a low-salt diet, and eat mostly whole, unprocess foods) AND do really intense cardio sessions (3 times a week for 30 mins is good) that will burn a ton of calories and keep your metabolism elevated (continuing to burn calories) for hours after your workout. Yoga, pilates, walk, running, biking, plugging away on an eliptical are not intense enough to accomplish this---they are all great for heart health and will burn extra calories while you are exercising but will not give you the multi-hour post-workout metabolism boost that you'll need to really burn fat off. Things that CAN give you the metabolic burn: hill sprints (basically sprint intervals where you sprint up and hill and then walk back down and repeat, over and over), intense circuit weight training--rotating exercises so you can take only 30 mins rest between sets (example - 1 set of pushups, rest 30 secs, 1 set deadlifts, rest 30 secs - until you get to 3 sets of each exercise completed...then move to rotating jacknifes and standing shoulder presses for 3 sets ea, etc), metabolic intervals--basic bootcamp type exercises (some gyms have bootcamp classes you can take, but you can easily do these at home too with nothing more than a stopwatch--google metabolic interval training for ideas), AND/or - kettlebell workouts (not many gyms offer these classes, but you can buy a kettlebell--or a couple so you have different weights--and a DVD and do them at home.
PS - I used to primarily do cardio and yoga and couldn't get rid of my tummy fat. Now when I go to yoga class (every time!!!) people ask me if I am an dancer (I never got that question before). What do I primarily do now? Power lifting and metabolic intervals.
