Will be a tattered weed, of small worth held. Were an all-eating shame and thriftless praise. Proving his beauty by succession thine.

What does tattered weed mean?

When the youth is forty years old, he will be nothing but a "tottered weed" (meaning tattered garment), "of small worth held" because he will be alone and childless.

When forty winters shall besiege thy brow refers to?

'When forty winters shall besiege thy brow' by William Shakespeare addresses the need to have children as a way of guaranteeing one's legacy and beauty. The speaker addresses the Fair Youth, informing him that in short order he's going to lose his beauty and his face is going to look like a plowed field.