How big were the tablets?
The British Museum exhibits stone and clay tablets from several cultures over the relevant span of OT time and locations. The tablets are typically no larger than a modern mobile phone, and smaller ones comfortably fit in the palm of a hand. They appear strangely modern.
Typically 1cm or so thick.
Stone ones white. Clay ones reddish brown - clay ones were erasable and reusable, or could be fired.
Not much space for writing, and in more primitive examples language was mostly symbolic. Surprisingly small characters so as to fit and quite fine work needing good eyesight. Even so, limited space for expression.
So yes, a few of those could be carried in the hand. And could be readily moved up/down a mountain about the person.
Also Exodus 32:15 refers to the original tablets (i.e. the ones Moses threw from his hands and broke) being carried in the hand, written on both sides. The British Museum exhibits small tablets, written on both sides. It also exhibits several such broken tablets, which seems to demonstrate they could be readily broken, for example by throwing to the ground.