Fried tofu is much better than not eating (slice it into strips and cook some crispy flavor in), and boca burgers wouldn't even be that bad either. Chances are, no matter what your sister makes you eat, it's not any worse than a lot of the stuff I have to eat on a regular basis, so don't feel too bad.
Also, it sounds like a lot of what's causing you to cry is a perceived lack of control over your life. Other people seem to dominate every aspect of your life, while you're simply left to suffer. If that's how your situation leads you to see your life, then you're going to end up more than a little messed up in the head -- maybe even permanently. Check out research on learned helplessness to get an idea of what I mean. Unfortunately, nobody in your household cares enough to help you out, so you're pretty much screwed.
You could try finding aspects of your life that you can control, or that give you more control, even if it means more stress. Part-time jobs are especially great in this regard (just avoid working in fast food). Having a car is another big one. You don't sound like a real go-getter though, and getting a first job can be a real tough hustle sometimes.
Ultimately though, if you can just develop a mindset that gives you a strong sense of control and direction over your own life regardless of the circumstances or the people around you, then you can more calmly deal with the problems of your sister and your household life in general. Not to mention, later in life when faced with hard challenges, you'll be much more capable of overcoming them.
But you're just a teenage kid, so that kind of highly developed mental state is pretty much out of your reach, especially if you're a teenage kid trying to get there on your own. Instead, try not to get too messed up in the head, and when you move out as an independent adult, try to repair the damage a little.
Also, just out of curiosity, what does your sister do to try and lose weight and be healthy?
The key to healthy weight loss is a little bit of strength training for toning and to increase your metabolism followed by a pretty good amount (2-3 miles at least) of somewhat intense aerobic exercise like running to use up energy and burn fat. Repeat every other day, and you can still eat like a normal person (to include some fast food) and still lose weight well into your 20s. If you still don't lose weight, then the next key is to eat just a small amount in the evening and not to eat at night, which, as long as you exercise, works even as you get older. And don't worry if you stop losing weight after that. Anything more will probably lead to unhealthy weight loss, and chances are you've found your healthiest weight at this point, so congrats.
The real reason to eat "healthy" foods is nutrition, so your body doesn't wear out and you aren't as likely to get cancer or diabetes (or gout or something). Furthermore, starving yourself on an irregular basis (i.e. skipping a few meals one or two days a week) actually drives weight gain, as it makes your body try harder to store most of the food you eat as fat rather than use it as energy for the week or so after you suddenly stopped eating.
If you really want to mess with your sister, you ought to take up running to get rid of the stress, while eating the foods you want to eat, and see if you can make her fat by getting her to alternate between eating more of what you're eating and not eating. Then as you achieve her dream image (or at least a better body image than she has), she'll go insane and leave the household feeling disgusted with herself and inferior to you.
And even if that doesn't work, you'd have a lot more physical power and endurance, plus you'd feel better. If you have a hard time finding a place to run, don't forget that you can always stay after school an hour or so and use the track and shower there, and then if you're only a few miles away, walk home.
