Learn Russian: Девушка устала носить тяжёлый рюкзак на спине. - The girl got tired of carrying a heavy backpack on her back.

Носить is the multidirectional verb for carrying on foot. We use it here because she is carrying the backpack around in general, perhaps hiking or walking in different directions over time, rather than making a single, focused trip from point A to point B. It emphasizes the ongoing process and burden of carrying the heavy load.

I thought носить means 'to wear' clothes. Does it mean 'wear' or 'carry' here?

It can mean both! While you often see носить used for wearing clothes, its core meaning is to carry something around on foot. In Russian, wearing clothes is essentially 'carrying' them on your body. Since a backpack is a heavy object supported by your back, 'carrying' is the best English translation, but the Russian concept is exactly the same.

Why doesn't тяжёлый рюкзак change its ending if it's the direct object she is carrying?

It actually is in the accusative case, but it looks identical to the dictionary form. The verb носить takes a direct object in the accusative case. Because рюкзак (backpack) is a masculine inanimate noun (not a living being), its accusative form is exactly the same as its nominative form. The adjective тяжёлый (heavy) follows the same rule.

Why does спине end in -е?

It is in the prepositional case. The phrase на спине answers the question 'where?' (on the back). We use the preposition на with the prepositional case here to show the physical location where the backpack is resting.