Learn Russian: Мой чемодан более лёгкий, чем твой рюкзак. - My suitcase is lighter than your backpack.

Because we are using the word чем (than) to make the comparison. When you use чем, the second item in the comparison takes the exact same case as the first item. Since мой чемодан is the subject (Nominative case), твой рюкзак is also in the Nominative.

Could I use the short comparative word легче instead of более лёгкий?

Yes! You can say Мой чемодан легче, чем твой рюкзак. In fact, using the one-word short form (легче) is generally more common in everyday spoken Russian than using более (more) with the long adjective.

If I wanted to compare without using чем, how would this sentence change?

If you drop the word чем, the second item must change to the Genitive case. The sentence would become Мой чемодан легче твоего рюкзака. Both ways of comparing mean the exact same thing, but you can only do this Genitive shortcut with the short comparative form (легче), not with более.

Why is there a comma before чем?

In Russian grammar, you must always put a comma before the conjunction чем when it connects two parts of a comparison. This is a strict punctuation rule that differs from English.