Something that's valuable and heavy is extremely precious and probably even more valuable than your less heavy things.

貴重 is used especially when something is rare, important, or hard to replace. You can use it for physical things, but you'll see it used to show appreciation for intangible things too, like 貴重なご意見 (your valuable opinion) or 貴重な体験 (a precious experience).

This is a jukugo word that uses the on'yomi readings of the kanji. You didn't learn this reading for 重 with the kanji, so here's a mnemonic to help you:

Keep things precious to you very close, because the evil Mrs. Chou (ちょう) will come and steal them away if you don't. She'll take all the valuable things you have and destroy them.