Moshe descended walking backwards down Har Sinai, facing the cloud of Hashem. The Luchot, which weighed 40 seah, were suspended in the air slightly above each of Moshe's hands. And the two (6x6x3) Luchot were separated from each other by two hand-breadths.
Moshe only grabbed hold of the Luchot to smash them, after their holiness left due to the sin of the golden calf.
Rabbeinu Chananel, on Shemot 32:15
ויפן וירד משה מן ההר. We learn from this word ויפן, he turned around,
that Moses descended while facing the cloud just as he had done when
ascending the mountain. In other words, just as he had ascended facing
the cloud, he now descended keeping his face toward the cloud, walking
backwards.
The Or HaChaim, on Devarim 9:17
ואתפש בשני הלחות ואשלכם, "and I took hold of the two Tablets and I
flung them, etc." Why did Moses have to mention that "he took hold" of
something which was already in his hands? Perhaps as long as the
Israelites had not yet been guilty of sin the Tablets were suspended
in the air slightly above Moses' hands so that he could not actually
touch them. This may be what is meant when we were told in verse 16:
"and the two Tablets of the covenant "were above my two hands." Moses
had not said that the two Tablets were "in his hands." They seemed to
carry themselves. Once Moses espied the golden calf, the Tablets lost
their holiness so that Moses had to "take hold of them" with his
hands.
Talmud Yerushalmi, Taanit 4:5:2
Rebbi Samuel bar Naḥman in the name of Rebbi Jonathan: The tablets
were six hand-breadths long and three wide. Moses held two
hand-breadth, the Holy One, praise to Him two hand-breadth, and two
hand-breadths of space were between them. When Israel sinned in that
way, the Holy One wanted to seize them from Moses’s hand, but Moses’s
hand had the better of it and seized them from Him. That is what the
verse praises him at the end and says, and all the strong hand, peace
shall be on the hand which had the better on mine. Rebbi Joḥanan in
the name of Rebbi Yose ben Abbai: the tablets wanted to fly off but
Moses held them, [as is written,] I grabbed the two tablets. Deut.
9:17.
It was stated in the name of Rebbi Nehemiah, the writing itself flew off. Rebbi Ezra in the name of Rebbi Jehudah ben Rebbi Simon: The tablets were a load of forty seah but the writing was carrying them. When the writing flew off they were too heavy for Moses’s hands, they fell, and broke.