Step 1: Reviewing the Surrounding Verse Context:
Milton asks, “What need'st thou such weak witness of thy name?” directly after describing physical monuments (“piled Stones” and the “Pyramid”).
Step 2: Explaining Why They are 'Weak':
These physical structures are called “weak” because they only witness the name of a person in a cold, silent, and inanimate medium (stone). They cannot convey the living beauty, depth, and intelligence of Shakespeare's actual writings.
Step 3: Defining the Referent:
Therefore, the “weak witness” refers to any man-made, physical, and material monument, such as grand tombs, pyramids, or piled stones.