I think the phrase “bend one’s eyes” comes from the old belief that the eyes “shoot out beams” to see objects. And “bend” was a common word for pulling the string of your bow and holding it before shooting your arrow, fixing your eye on the target. So to bend one’s eye does not mean to shape it in a curve, but to fix it straight ahead on something: therefore to stare steadily or intently at, to “fix” one’s eyes on, almost as if the were attached to the thing you’re looking at.