It's important to gain muscle for weightlifting. Fat doesn't lift things, but higher overall mass can provide a more stable foundation for lifts. In case you are wondering, you can get too fat to perform the lifts properly. In an ideal world, you will start lean (in the 10-12%), and dial things down when you edge up towards 15% body fat as a man. Add at least 5% body fat if you are a woman.
That said, different rep ranges target a higher proportion of different types of muscular adaptation. All are necessary to getting stronger, and over time you'll probably alternate your focus.
- 1-3 reps: power range. Typically with 90% of your 1 rep max or more intensity, targets primarily the miophibrilar hypertrophy. Pros: this is where you truly increase the amount you can lift. Cons: prolonged life in the 1-3 rep range with intensities of 90% or more of your max can wreck your body (injury, fatigue, etc).
- 4-6 reps: balanced range: Slightly lower intensities, targets a pretty balanced mix of miophibrilar and sarcoplasmic hypertrophy. This is a great rep range for beginners because it gives them everything they need to get started. It's also really good for just building up volume work.
- 8-12 reps: size range. Typically in the 70-80% range, targets primarily sarcoplasmic hypertrophy. This gives you a good foundation of useful size to build more strength from.
- 16+ reps: endurance range. Typically below 70% intensity, targets the ability of a muscle to grind out reps.
All of these play an integral part in increasing your max to help you get stronger. As a beginner, you will see plenty of increased strength without much change to the size of your muscles. That's because your body has a lot of untapped reserve that it's now getting ready for you to use. Eventually that runs out. As the weight you lift gets heavier, you start having more fatigue that takes longer to recover from. That's when you need to structure your training differently.
- Miophibrilar Hypertrophy is the bread and butter of strength. Essentially it is more contractile protein pairs, which essentially means more power.
- Sarcoplasmic Hypertrophy is the energy systems to feed your contractile proteins. Essentially, an underdeveloped energy system will limit your ability to push or pull heavy weights because the muscle runs out of gas before you are done. It also tends to take up a lot more space, so it increases your muscle mass visibly. Bodybuilders intentionally take advantage of that fact.
- Endurance is the ability to keep working in a fatigued state. Sometimes your one rep max is a real grinder. The difference between making the lift and missing it is the ability to keep grinding through the sticking point.
You need to gain muscle mass over time to lift bigger and heavier weights. It takes time to work up to this point, and to work through it. Multiple years of dedicated and intelligent work will help you see your goals. As a general rule, you aren't going to see someone with a 400lb or higher bench press that has small arms. It just doesn't happen unless in rare exceptions. The same holds true for someone who can squat 600lbs or more. They are just big--but not necessarily fat. They've put in time under the bar, increased their size and increased their maxes.
One way to think of it is that muscular size represents strength potential. It's up to you to put in the work to turn that potential into reality.