I’ve been wondering that in sentences like:
By lifting weight you can toughen those muscles of yours.
He is a friend of mine.
Why won’t we simply say:
Do they have a conspicuous difference in meaning? If yes, in which situations should we use the first form?
In the context that you provided, both forms are fully interchangeable. In my opinion, using the form "of mine" has the benefit of sounding more sophisticated.
By lifting weights, you can strengthen those muscles of yours.
By lifting weights, you can strengthen your muscles.
Other situations that the first form is necessary includes "something of mine" (used in sentences linked here: https://ludwig.guru/s/something+of+mine).