I've discarded the tables (writing tablets) you gave me because I've inscribed you into my brain and heart; these internal records surpass any physical memorial.
Charactered means both 'engraved' (as on tablets) and 'written as characters'; memory is here a physical, inscribed thing.
The speaker claims that the beloved's 'gift, thy tables, are within my brain / Full charactered with lasting memory.' The brain has become a writing surface, the beloved's image 'charactered' (engraved, written) upon it. This record shall 'above that idle rank remain / Beyond all date even to eternity.' The beloved is inscribed not in wax tablets but in the speaker's neural permanence—a medieval understanding of memory as physical engraving.
The couplet explains the apparent rejection: by giving away the physical tables, the speaker trusts them to 'those tables that receive thee more'—perhaps the speaker's own written words, or simply the beloved's continued existence. Giving them away becomes an act of confidence, not dismissal. The speaker needs no tally or retention aid; the beloved is so completely internalized that physical memory aids would be redundant, even an insult to the perfection of internal inscription.
Someone gave you a beautiful handwritten letter, and you kept it for years. But eventually you realized the letter itself didn't matter—what mattered was that their words were completely internalized, part of how you think. The physical object became unnecessary.