Lines 37-40 Summary

Get out the microscope, because we’re going through this poem line-by-line.

The Catterpillar on the Leaf
Repeats to thee thy Mother's grief.

This is tough. Blake was always neck-deep in the Bible. It was his favorite book, and without constantly having the Bible in mind the way he did, it's impossible to figure this one out. (Even if you are constantly thinking about the Bible, it's still probably really difficult.)
In this case "thy Mother" is actually the mother of all humankind (according to the Bible's version of events): Eve. A snake (or, the Devil), as almost everyone knows, tricks Eve into eating an apple, then it's chaos and suffering and confusion for humanity from there on out.
So what does this have to do with a caterpillar? Well, it's complicated. But try this on for size: as Blake understood the Eden story, after Eve and Adam eat from the apple (which is a symbol of "the knowledge of good and evil") they fall from a higher spiritual realm that Blake calls "Innocence" into the world of "Experience": the messed-up world we all live in.
The caterpillar repeats Eve's grief at eating the apple, because it's trapped in the world of experience—instead of being a spiritual being living in a better world, it's just another caterpillar, one in a trillion, hustling to get by.
Also, it's destructive, since it eats leaves and flowers to survive.
Weird? You bet, but does it make sense? If you look at everything else Blake ever wrote, it does.

Kill not the Moth nor Butterfly,
For the Last Judgement draweth nigh.

This couplet isn't too different from those we've seen before. It also deals with insects, like the three that came before it, and it's also attacking animal cruelty.
In the same way that the boy who kills the fly ends up learning what it's like to be attacked (and probably killed) by a spider, this couplet says that people who go around slaughtering moths and butterflies are at the risk of experiencing "The Last Judgment." They're going to need to pay for their sins.
This also fits in with the "world in a grain of sand" thing—butchering butterflies might, in the grand scheme of things, seem like small potatoes. But, according to Blake, it's causing the Last Judgment to come down—it's bringing about the end of the world. Blake means this in a metaphorical way—cruelty is going to bring cruelty back against you (like in the couplet about the boy killing the fly).