Kon really really empathizes with Fate. Like, really, really, and honestly he kinda sees other clones as something akin to his "kind," his species, even if they're another species or something.

So he totally is like 100% there in looking out for her, and aside from that, he just likes who she is and thinks she's tremendously strong for being as kind and sweet as she is, given the circumstances.

If he'd actually grown up under Luthor's care and been treated by him the way Fate was treated by Precia, he'd have probably wound up a total, evil nutjob.