Quote 1
But I have a son, sir by order of law,
some year elder than this, who yet is no dearer in
my account. Though this knave came something
saucily into the world before he was sent for, yet was
his mother fair, there was good sport at his making,
and the whoreson must be acknowledged.—Do you
know this noble gentleman, Edmund? (1.1.19-25)
Here, Gloucester reveals that, in addition to his illegitimate son, Edmund, he also has another son "by order of law." ("By order of law" just means Gloucester's other son is legally recognized as a legitimate heir. In other words, this other son isn't a "bastard" like Edmund. Or Jon Snow.)
What's interesting about this passage is that Gloucester says he doesn't favor his legitimate son over Edmund. Gloucester's legitimate son, he says, "is no dearer in [his] account." We can't help but notice that the play is full of speculation about which children are most beloved by their fathers. Recall from a previous passage (1.1.1-6), Kent and Gloucester wondered which son-in-law King Lear liked best. And we know that Lear favors Cordelia over Goneril and Regan.
We should also point out that the more general question of "who loves who the most" turn up again when King Lear stages a love test, demanding to know which daughter can say she loves her father more than everyone else. Seems like Shakespeare is raising the following question: Is love (especially family love) quantifiable?
Quote 2
GLOUCESTER reads
This policy and reverence of age
makes the world bitter to the best of our times, keeps
our fortunes from us till our oldness cannot relish
them. I begin to find an idle and fond bondage in the
oppression of aged tyranny, who sways, not as it hath
power, but as it is suffered. Come to me, that of this I
may speak more. If our father would sleep till I waked
him, you should half his revenue forever and
live the beloved of your brother. Edgar.'
Hum? Conspiracy? 'Sleep till I waked him, you
should enjoy half his revenue.' My son Edgar! Had
he a hand to write this? A heart and brain to breed it
in?—When came this to you? Who brought it? (1.2.49-61)
When Gloucester reads the fake letter that Edgar supposedly wrote to his brother, Edmund, he seems ready to believe that his son would conspire to kill him. But why? Shakespeare explores how Gloucester's relationships with his two sons dramatize some common issues surrounding primogeniture (the system by which eldest sons inherit their fathers' wealth, titles, lands, power, debt, etc.).
The letter proposes that the brothers kill their father so they can share Gloucester's wealth ("revenue"), which gives voice to a common fear that all sons look forward to their fathers' deaths. This kind of anxiety can also be found in other plays like Hamlet and Henry IV Parts 1 and 2.
Quote 3
GLOUCESTER
As flies to wanton boys are we to th' gods;
They kill us for their sport. (4.1.41-42)
This is one of the most famous lines in the play. For Gloucester, the gods are not only indifferent to human suffering but they're excessively cruel, causing human misery just as easily and thoughtlessly as "wanton boys" might swat at "flies."