The Yerushalmi in Taanis says that the letters kept the luchas light to be able to carry. The letters flew off, so it became so heavy that Moshe Rabbenu could not carry it and he drop it. This seems to argue with the Bavli where Hashem commended him that he drop it. Maybe, there is a proof to the Yerushalmi. It is written as dropped from one hand but read as both hands. He was holding it in one hand but when it became heavy, he held it with both hands but it was too heavy to be able to hold it.
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