Your brother is but young and tender; and, for your love, I would be loath to foil him, as I must, for my own honour, if he come in: therefore, out of my love to you, I came hither to acquaint you withal; that either you might stay him from his intendment, or brook such disgrace well as he shall run into; in that it is thing of his own search, and altogether against my will.
There are no more uses of "loath" in the play.
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loath to admit a mistake
Much as they loath to admit it, there are serious divides splitting the party.