Huicke and Katherine are both outsiders at court. Huicke because of his skin disease and sexual orientation and Katherine because of her intellect and her seeming desire not to want to be there. Huicke took a risk admitting the true purpose of his visits to Katherine, but he seemed to realize it was an opportunity to forge a rare friendship with someone who shared his intellectual passions. It may also have been be quad he knew that the king was romantically interested in her which meant she had the potential to have influence at court. I don't think that was the primary reason, but it could have influenced the risk he took.