Wow! your puppy is very tiny! my baby is 2.5 lbs at 5months. Free-feed her if you must. I agree with the others, you're probably feeding him too much for his little stomach. But what is important, is you get something in her stomach several times a day. And always keep NutriCal or Nutripet at hand, it can also increase appetite.
I do not free-feed my baby (I feed her 3X a day) because I don't have to. She finishes every serving one at a time. If I give her her daily amount at once, she might finish it up instantly and I don't want her not eating anything for long hours.
By the way, when I first got my puppy she hardly ate the dog food the breeder gave me. It's not a very good brand. So I had to mix in boiled chicken liver to it so she would eat. That was for 2 weeks. But when I switched to a premium brand, there's no need for mix-ins. She can't wait to have her food while I'm preparing it!
Goodluck on your new puppy! I hope you find out what works for you and your baby soon