I don't just love Adam West because of the humor. I find there's more to him than that.
His Batman embodies a truly great hero, moral, selfless, smart, and with a heart. You cannot beat the friendship and camaraderie he has with his "old chum" Robin. He loves old Alfred, and sweet blissfully ignorant Aunt Harriet. How can you not love when he and Robin arrange for her to meet Batman and Robin on her birthday as a surprise, and give her a kiss on the cheek before they leave. I know that on paper that sounds cheesy but the actors made it work so well as a genuinely touching moment. His respect and friendship with Gordon and O'Hara is second to none. When Neil Hamilton's Gordon says "Our only hope is the caped crusader" you believe it.
He has the duality, as his Bruce Wayne is so straight edged, acts like a helpless fop in times of crisis, totally plays up the whole philanthropic business man side. He extends the hand of help to some of the poor misguided molls who worked for the villains after they see the error of their ways to help them rebuild their lives and get a fresh start. His Bruce Wayne has lost his heart and gotten it broken (see the Batman movie). Shunned chances to be in a relationship because he puts his crime fighting life first. His chemistry with Catwomen Meriwether and especially Newmar was fantastic.
Sure there's heaps of camp associated with West's Batman, but there is heart and emotion there, too, and a lesser actor would have looked totally ridiculous trying to do that in a predominately campy show, but West pulled it off big time, IMO. It's one of the many reasons why he has endured as a cult icon and fan favorite, even in the face of so many new darker Batmen, West has endured.
No wonder Bale loves him best. West is one of my favorite live action Batmans, second only to Bale.