VET!! Distemper can mess with the nerves -- and too much of a dog's digestion has to do with neural transmission of information to the brain ("ok - protein ready to go to blood, ok ... ALL protein gone now, send some of this to the small intestine, ooh, need more enzymes ...")
I'm no vet, but I do know that when a dog isn't gaining weight and he's eating like a little piggie something might be wrong.
Tapes are EEE-ZZZZZZZ to treat. Now they might come back but your vet may simply choose to give him a dose of med (and you can *not* get it over the counter -- tape worm med is a different stuff!) and *see* if that fixes it. If it IS tapeworm, left untreated he'll eventually starve to death - the tape gets longer and bigger and eats more and more.
Take a FULL fecal to the vet. You can't catch tapes on just the little rod that they snag an internal sample with -- they can be tough to 'find' BUT give the vet all he needs to work with. Watch him, and snag and entire poop in paper towel and put in a ziplock bag. If you are more than 5 minutes from the vet put it in a bigger plastic bag that zips (double bag it) and put it on ice. Or keep it in the fridge over night and THEN get to the vet a.s.a.p. in the morning. Sorry -- that's gross but this would be the cheap way to diagnose this.
The other thing the vet might suggest is something like Pro Zyme (or ask about it) -- that's enzymes that help the body digest the food better so they get more 'good' out of their food. But it's no cure if the body is dumping stuff into waste that hasn't been digested properly.
The vet might want to do some bloodwork -- he's a distemper boy so you'll have to track things a while to make sure there wasn't damage done by the virus that you haven't caught.
A puppy HAS to gain weight -- it's part of growth and gaining muscle mass. If money is a concern, TELL the vet. Then they can do things in a logical order (and in order of what might be cheapest to deal with).
Good luck. And good for you -- bringing a dog thru distemper is NO picnic and you've done a good thing. Sometimes it's just figuring out what you gotta do for THIS dog.
I wish I could be more specific, but telling me how much he eats without knowing exactly what breed and size he is ... *wrinkling nose* I'm not that good at remembering everybuddy's pup. Sorry! Good for you for watching him so close!!!
"The best and most beautiful things in the world cannot be seen or even touched. They must be felt with the heart." Helen Keller