How does King Lear mirror the character of Gloucester?
Gloucester is King Lear's foil. This means that in some way, he reflects the protagonist, highlighting his dominant characteristics. Gloucester has often been belittled for not being a full character, as being little more than a cipher through which the dramatic needs of the play are expressed. There's an element of truth to this criticism. Gloucester's ordinariness and prolixity as a character continually allow Lear to give full vent to his larger-than-life personality in all its tortured complexity. But, in being constantly overshadowed by his king like this, we're able to appreciate Gloucester as a more recognizably human character, someone for whom we can share both sympathy and empathy.
The fraught relationship of Gloucester to his sons neatly parallels that of Lear to his daughters. Initially, both men are blind as to the respective virtues of their children. It's only over time that they become disabused of their fatal misunderstandings. Lear comes to see that it was Cordelia who really loved him all along, despite her being the only daughter who wouldn't publicly profess her love. And it's only when Gloucester is blinded that he understands the true nature of Edmund, and that he lied to him about being betrayed by Edgar.
Both men give, but for different reasons. Lear divides up his kingdom among his daughters, yet cannot let go of his overweening sense of greatness nor the need for affection, which he feels is his due. Gloucester, however, gives freely, whether it's unswerving loyalty to an ungrateful king, or to an equally ungrateful son, or the simple act of giving some money to Poor Tom, who, unbeknown to him, happens to be Edgar in disguise. (It's worthy of note that Lear gives Poor Tom absolutely nothing.)
Lear is the architect of his own downfall; Gloucester is the victim of circumstance. Both men suffer enormously: Lear, from insanity; Gloucester from blindness. Yet, despite his incapacity, and various travails, Gloucester still manages to retain an astonishing degree of faith in human nature. Contrast this with Lear, whose madness brutally manifests itself in a venomous hatred towards the world. Extreme adversity brings out the best in one man; the worst in the other.
Despite his numerous flaws, Gloucester is clearly a character of much greater moral integrity than Lear. Because of this, his sufferings are greater, but at the same time more identifiably human, than those of the king to whom he gives such undeserved loyalty.
King Lear and Gloucester are both manipulated and deceived by their evil child (or children) and blind to the love of their loyal and good child. Both have been powerful for so long, one as monarch and one as an earl, that their ability to discern deception from truth has become dulled.
In Lear's case, he mistakes the extravagant words of love from his two elder daughters for real love. He simply cannot understand that it is his kingdom they love, not him as their father. They will say anything to get his power.
Cordelia, in contrast, is so disgusted by her sisters' transparent use of flattery that she only provides the bare-bones facts of her own loyalty and love. This enrages Lear so much that he banishes her, the only daughter who truly cares about him.
Gloucester also cannot tell the difference between appearance and reality. He lets the deceptions of his illegitimate son, Edmund, who is angry that his birth status keeps him from inheriting, turn him against his honorable son, Edgar.
Through both Lear and Gloucester, Shakespeare explores how the unchecked ambitions of the young and the lack of discernment of the older generation can tear apart families. By placing two families in a similar situation and making characters of both genders equally capable of evil, Shakespeare suggests that putting ambition ahead of compassion is a societal problem.
When two characters mirror each other, those characters are called foils of each other. The purpose of a foil is to emphasize certain characteristics.
Lear and Gloucester foil each other in a few ways. First, their families are nearly identical.
The issue of blindness also makes the characters foils of each other. Gloucester is blind to the truth while Lear becomes literally blind in the end of the play.
It can also be argued that both characters are defeatists, but you would have to find evidence for that.