I completely forgot that I had posted about this. Thank you so much for your replies and thoughts, and I'm sorry I didn't get back to this thread sooner.
I think that my cat might, as you all suggested, have been responding to myself, my husband and things in his/our environment. My husband ended up in the hospital for 5 days beginning a few days after my original post, so it may be that our cat was sensing my husband's poor health before it was apparent to us and was seeking comfort and reassurance. I, too, have had some health issues the past month that resulted in a major surgery 2.5 weeks ago, and my cat has been very "attentive" thoughout this time.
I think it seemed odd to me because our other cat, and all cats I've had previously, seemed pretty independent - but this cat seems to want more and more attention as he gets older (he's about 11 years old now). His appetite and litter box habits have all stayed the same though, and a recent routine vet visit showed no problems, so I think I'll just cuddle more and worry less.
Thank you very much for your advice.
maita - I think a friend for your kitty could help enormously if you could manage it!