I'm 5' 2" and weigh between 158-163 (fluctuates over time). I'd like to try to pull down to hover more around 150, but mostly due to my current sport of choice (figure skating) - less weight means less I have to jump into the air

I can't go by the charts which all tell me I'm overweight based on my height/weight ratios because those formulas don't take into account actual lean muscle mass, which I have more than the average person due to my training. One thing I learned for weight loss is the following:
1. Less calorie intake (the obvious), but not only concentrate on the quantity of food, but the quality of it. (Why is it that you only feel like eating one banana, but a whole box of chips...? The better the food, in general, you naturally will eat less because it provides your body what it needs with less intake.
2. Increase cardio - evaluate what cardio exercise you are doing, and find a way to increase it (add an extra day, extend current sessions an extra 10-15 minutes). By upping activity slowly, it increases your chance of successfully incorporating it as a habit rather than trying for a max routine and slowly giving it up.
3. Weight/Strength training - this is needed to increase muscle mass which allows your body to burn calories more efficiently - plus it just makes you healthier and more energetic. This can be traditional weights, or could be programs like pilates or yoga.
What I found when incorporating #3 into my routine, depending on how much strength training you do, you may go through a phase where your weight appears to go up vs down - and that will mainly be due to the fact that muscle weighs more than fat - so don't panic. If that happens, judge by how you feel and how your clothes fit. It the scale goes up, but your waistline seems to be going down - you're going in the right direction.
For cardio - I found using an activity I found fun to do as the best way to make it a habit. First was ballroom dancing (in fact most any dancing will get your heart rate going), then rock climbing, now it's figure skating. If you find some activity (like martial arts, team sport, dancing, anything that gets you moving), and it's something you've always wanted to do or learn, you'll be more apt to put in the effort to keep with it. Then as you are learning and improving in the sport, the side effect is usually your weight going down. To what degree depends on the sport and how often you participate (as well as how well items #1 and #3 are doing in combination

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Pretty much the same old/same old everyone says - making the decision to commit to this is the first step, then consistency with sticking to it is the second. Don't weigh yourself every week or so, make it more of a monthly or quarterly check in - that way you won't get as discouraged by the week to week fluctuations that often will occur.