Not weird at all. I have two cats myself, and I would love for them to sleep on our bed. The only reason I always keep them out of the bedroom is that last year when they were still kittens one of them seemed to think the bed was a toilet and peed on it about three or four times! So the bedroom is off limits for them unfortunately.
But I've had friends growing up whose cats slept on their beds with them, and when I was housesitting once I'd often wake up to find the people's cat curled up on my feet or legs... the warm weight is a nice comforting feeling. I don't like dogs on the bed though (mostly I hate the smell), and our dog is an outside dog anyway (German Shepherd).