Let the hate flow through you...
(Sig's an Amon Amarth lyric.)
Punch is momentum. Momentum is velocity times mass. Which is why you can't block a bullet with your hand, it's tiny, weight measured in ounces, but moves at an extremely high speed. Conversely, you can't stop a 30,000 lb rock coming slowly down the hill, speed is not great, but it's mass is so huge that it does not require much speed to have very high momentum. And a rock that size hitting earth at a high velocity has so much momentum that the shockwave will knock people down many kilometers away. Remember, mass and velocity. If either one is low, you must compensate with the other.
Unfortunately, when it comes to hitting, it is your muscles that accelerate your limb. If you are a 90lb kid, those muscles will be relatively small, and the weight of the hand, with shoulder and hip behind it, will be considerably lower than that of a 175lb guy. So, say a 175 guy has 60 lb of meat behind a hit. He doesn't have to accelerate it very much in order to knock the other guy down, it's already got plenty of momentum due to sheer weight. A 90lb guy who can only put 30lb into a hit, has to accelerate it considerably, and that acceleration comes from muscles, and a 90lb guy won't be very well muscled, unless he's very short. More importantly, you would not be able to block at all. This is again simple physics, called inertia, the affinity to remain unchanged. When you are 200lb and someone punches you, you are 200lb of meat and bone very reluctant to move in the direction of the impact. It'll take a very hard punch to shove you in that direction. If you are 90lb, it'll take considerably less force to send you flying.
And by the way, 175lb is "an average guy". If you are 6' tall, average weight for a man that size is 170lb. So 175 is *slightly* heavier. Arnie, with almost zero fat, was 260 lb, if I remember right, while average weight for his height was around 180 lb. That's a bodybuilder. 175lb is just a reasonably fit guy who never even touches weights, just eats healthily enough, has a physically demanding job or just does basics (pushups, pullups, dips, situps and jogging) using his own body weight. If you got him to drop all the fat, he'd drop down to 150lb, the assumption being that the 90lb guy is already not fat.
The difference that comes with practice is that that a 90 lb kid can put all 90 lb into a kick. I love Jeet Kune Do for that, a small guy who lands a solid side kick can send the heavier guy flying, because you put almost all of your body mass into that one hit. However, you must remember that even if you sock the 175lb guy, he has enough mass and inertia to soak up your hit, while being 90lb you won't soak up many of his. What's more, a 175lb guy can probably block or deflect your kick, since he has the mass to do so, while you being 90lb probably won't have enough mass to block or deflect his.
So this whole "I'm 90lb and will beat a 175lb guy with training" is wishful thinking. With enough practice, and on your terms, with strict rules, you may have a shot. In real life, he'll bulldog you against the wall and pound you flat, and that will be the end of it. 85lb difference is enough of an edge.
Doesn't mean a scrawny guy can't win, he just has to know where to hit, how and how hard. The self-defense guys will advocate going for eyes, ears, windpipe, groin, solar plexus, etc. It's fine if it is a life or death situation, but for a schoolyard brawl, do you want to end up in jail afterwards? If you poke a guy's eye out or kick him in the lower ribs so hard that you break them and/or his liver ruptures, or accidentally cause a tracheal collapse, or miss his jaw and dislocate one of his spinal discs? What then? Not to mention the psychological aspect of it, the thing people mention the least, which is ironically what will affect you the most. No matter how much the other guy deserved it, if you cripple or kill the guy, even if purely by accident, you'll have to live with that for all the days of your life.
And, OP, don't open your mouth when you're about to get hit, and don't clench your jaw either. If your mouth is open, it'll snap closed or your jaw will be dislocated or broken. If it's clenched, there's a possibility of losing some teeth. And from personal experience, scars on the face seldom fully heal by themselves. Depends on how bad it is, of course. I know someone who bit clear through his lower lip at the age of 5, and still has that scar at the age of 25. Harrison Ford got a scar on his chin when he was 20, it's still there 40+ years later.
Most "kids", I use the word loosely here, punch first and then kick when you're down. Ideally, you want some basic boxing. It'll make you more effective with least time. Have someone with paw pads on work with you for a few weeks. You'll learn to dodge those punches, dive under them, punching accurately and footwork. People neglect footwork a lot, but it's the most important part.
Oh, and PS, don't punch the guy in the teeth, unless you want lots of scars on your knuckles, or an STD. I'm not kidding, you can punch a guy at some bar, knock his front teeth out and "win", only to die from AIDS a few years later because your skinned knuckles came in contact with is saliva. If you have gloves on, go for it, but bare handed, don't. Also, forehead is a big no-no. It's almost a solid bone. Like punching a concrete wall, it's why headbutting someone in the face works so well.
Anyway, good luck. I feel every boy needs some martial arts training around 8-10 at the latest. Before some douche suspects you're making a pass at his girlfriend, even if you aren't, and she isn't. It comes in handy. For me, it was boxing, and it was very handy indeed. Footwork more than anything, stepping past the guy trying to punch you and landing a solid right in his jaw is pretty much what you need to do ONCE in order to NEVER have any problems at that school again.