How we cite our quotes:
To say, within thine own deep-sunken eyes,
Were an all-eating shame and thriftless praise. (lines 7-8)
This is a tough line in the poem, but it's crucial. If it's a good thing to have kids, what's the alternative? What would the bad option be? Well, the speaker is saying that if you got old without having kids, you'd be left with only yourself to look at and praise. You would be stuck with only your "sunken eyes" to remind you of how good looking you used to be. Everything else would wrinkle and age. This would cause terrible ("all-eating" shame) and leave you miserable. Doesn't sound so great, huh?
If thou couldst answer 'This fair child of mine
Shall sum my count and make my old excuse,' (lines 10-11)
Fortunately, there's a solution. Here's the speaker's argument: you can build a family, and you will have someone to carry on your beauty. You won't have to look at your own eyes to remember when you were young, because your son will be a kind of copy of you. Wasting your beauty is like wasting money (being "thriftless," as he puts it in line 8). But if you have a family, you've "invested" your beauty wisely, and it will continue to grow in the form of your son.
Proving his beauty by succession thine! (line 12)
Inheritance was a big deal in Shakespeare's time, even more so than it is now. If you were a nobleman, you didn't just get money or property from your parents, you also inherited a title. So if this sonnet was written to a young nobleman, the idea of succession (following after your father) would have meant that you were legally entitled to whatever he had, including his beauty.