My untrained guess (for what it's worth) is that it probably had something to do with the mechanics of letter-writing; one would have to "re-fold" one's own letter once it was written, in response to a correspondent's earlier "folding". (Or perhaps Romans even wrote a reply on the opposite side of the sheet? It would make some sense as a way to conserve paper.)
It's clearly from the very last legal meaning, which is as explained here. Compare the synonym in the last quotation - resolvere, that is "to untie, unfold back something that has been tied or folded together, concluded by the defendant's previous statement". The defendant ties the case up, the plaintiff unties it again.
I'm not sure what type of material was used in the late Empire to present legal statements: replicāre implies wooden tablets (if not sheets of parchment) while resolvere must refer to a scroll. But since the meaning "to go over again in the mind" is earlier than this, the legal use is easiest to derive from this latter one without the need for a metaphor involving any written medium.