When you say "no matter how much I eat", have you ever actually tracked how many calories that is? Some foods are very filling on a surprisingly small number of calories, so it may be that you're not eating as much as you think you are.
The basic formula calories in = calories out will maintain you at your current weight. Eat more, and you'll gain weight; burn more, and you'll lose weight. If you're working out, at least some of that weight gain will be muscle.
As far as the exercise goes, a smaller number of repetitions at a higher weight is your friend. You should also be focusing more on the large muscles of the body than the small ones. While you might like larger arms, you'd be better served doing squats, lunges, deadlifts, rows, and benchpresses than bicep curls or tricep kickbacks. You also need to get over caring what the guy next to you is doing. You are at the gym to be a better version of you, not to be better than the man the next weight over. Most likely, he doesn't have a clue what sort of weight you're using, and doesn't really care either.
You also need time between workouts for your muscles to rest and recover. At least 24 hours, and even better is 48 hours before you use the same muscles again when you're doing anything with heavy weights. And for some exercises, like pullups and pushups, body weight alone is heavy weight.
As a formerly excessively skinny guy myself, I know the annoyance of being unable to gain weight. But you really do need to consume more calories if that's your goal, and preferably in healthier ways than a supersized fast food meal. Some simple ways of doing that:
Protein shakes. Most of the major brand names are pretty overpriced, but you can get some quality powder cheap from places like trueprotein.com
, where you're paying less than $5 per pound compared to GNC's charging more than $10 per pound. Blend it in milk, add some fruit or chocolate or peanut butter, and you can add a good amount of calories as a drink.
Trail mix. Basically, never let yourself get hungry. Dried fruit, nuts, healthy cereals (think along the lines of Cheerios or Chex) can generally be bought in bulk, and you can mix them up and carry around a ziplock bag and take a handful every so often.
Fruit juices. Not recommended for those trying to lose weight, as a fruit juice has nearly as many calories as a sugared soft drink, it's actually a pretty good choice when you're just trying to add calories to your diet. Nearly the same calories as a soft drink, but with more vitamins and minerals and whatnot.
Milk can be added to your scrambled eggs easily; and at your weight, unless you have cholesterol problems you can go with whole milk and whole eggs, instead of skim milk and eggwhites. So can cheese. Meat can be added to your pasta sauces, and to your salads. Olive oil or peanut butter on your bread tastes good. There are higher-protein pastas on the market that cost just about the same as a normal white pasta.
Track your calories consumed for a week on a site like fitday.com
and you might be surprised to see what you're actually consuming. Play around with some of the foods there to find a way to eat more without busting your budget.