1) MUSCLE IS MORE DENSE THAN FAT. Yes, it's true. A pound of lean muscle mass takes up less space than a pound of body fat. This means a couple of things. First, it means that to the extent body mass index is ever an accurate measure of obesity in individuals (which is to say, it isn't at all, as it was designed to measure obesity in populations) it is even less accurate for athletes, because athletes have more muscle and therefore will weigh more than a similarly built sedentary person. Second, it means that if you are beginning an exercise program from a sedentary lifestyle, you will be building muscle, and since muscle is more dense than body fat, any weight reduction from fat loss will likely be offset by the weight gained from muscle mass.
2) WATER AND BONE MASS ARE IMPORTANT PARTS OF THE EQUATION. This has to do with the size of your skeletal frame and your hydration level. Yes, you can lose water weight, and no, it isn't a good idea (with some medical conditions excepted). The better hydrated you are, the better your body can operate. You don't want to be too hydrated -- that can lead to a condition called hyponatremia -- but for purposes of this post, if you hear sloshing in your stomach when you walk, stop drinking. If your pee is darker than lemonade, drink some more. In terms of bone density, denser bones are heavier bones but they are also stronger bones, which means they are less likely to cause you problems with stress fractures. So if you (read:I) happen to be a 5 foot 9 woman with a large bone structure and you are well hydrated and muscular, you will not, I repeat NOT, ever weigh what the BMI says is a "normal" weight for you, barring cancer, anorexia, or some other wasting disease.
3) FITNESS METRICS ARE FAR MORE IMPORTANT THAN WEIGHT AS A MEASURE OF FITNESS. This seems elemental, but I'm always surprised at how many people don't get this. Size and fitness are not necessarily correlated (although they can be). Nor, for that matter, is speed and fitness (although, again, they can be). An example: at my 8k run, I was dead last. My pace was approximately 16 minutes per mile. The woman who finished before me had a pace of about 15 minutes per mile. I would estimate she was about 5'2" and weighed probably 225 pounds. Not thin, and by many people's measure, she'd be considered "fat." But she finished before me. Why? In part because she'd been working on her fitness for longer than I had. She'd walked a marathon at a 15.5 minute mile pace the previous fall. Did she weigh more than I did? Maybe. Was she more fit than I was? Maybe. That day, she was faster than I was. Fitness is a linear progression, not an end point; metrics are just one point on the line. If you are moving longer, faster, more efficiently than the last time you moved, congratulations. You're headed in the right direction. Ignore the scale.