A bathroom scale measures the pull of gravity on our mass. Scales that measure in pounds are actually measuring force, not mass. Force = mass x acceleration [F = ma]. When we stand on a bathroom scale, the acceleration is the acceleration of gravity.

You can test that your body has a downward pull on it by jumping and then landing back on the ground.

Here's a Scientific American article about exercise and muscle strength:
stronger muscles.

This article says that most of the muscle cell is the 2 proteins that pull on each other when you're using your muscle. The 2 proteins are actin and myosin. So if you have bigger muscles, you'd have more of the proteins that do the work of muscles.

But muscle size isn't always a measure of muscle strength:
size and strength in muscles.

From this site, you can read that physical strength might stem as much from exercising the nervous system as the muscles it controls. The findings could explain why those who lift heavier weights enjoy greater strength gains than low-load lifters despite similar growth in muscle mass.

I also found this serious and interesting article which you might enjoy reading:
Live Science.