Translation:This pocket watch is more than seventy years old.
When you use time as an age, you always use "avere" (ho, hai, ha, abbiamo, etc.) instead of "essere". It's just a rule that must be remembered.
Ho trent'anni = I have thirty years = I am thirty years old
You''d never say "Sono trent'anni" because the verb essere means that you "are" something, interchangeable with something. The "essence" of something, in other words.
Sono un uomo = I am: a man
Sono venti anni = I am: 20 years. Not really, you are 20 years old .
In the same way that you wouldn't say "I am a fox". You would say I am "as clever as" a fox.