I haven't read the responses, but basically, I had your exact situation: sleepy baby who didn't gain weight in the first two weeks, ped (and LC) recommending supplementation.
In my opinion, looking back, it was the sleepiness that did me in. That child simply did not nurse enough in those first two weeks to get my supply up and running, and by the time he stopped falling asleep at every nursing session, I was making only enough for him to maintain his weight, but not enough to gain. Every time I stopped supplementing him, to see if his newly wakened state would produce more milk, he just didn't gain weight.
However. That was my first child. You are an experienced mother with a successfull bf history, so you have a huge advantage on me. Here's what I would do. Give her the supplement. I don't care what anyone says, a 3 oz weight gain over two weeks is not enough, not good.
I would do the formula for 48 hours to rule out other issues, like the ped suggested. And in the meantime, pump like a madwoman. Pump like crazy to get your supply up. (I understand what a huge pita this is, especially when sleep deprived). Because I honestly think that a kid who falls asleep all the time - it would take me literally an hour to get my babe to "nurse" the equivalent of 10 minutes, what with trying to wake him up - is going to mess with your supply in those early days.
I don't think you are doing anything wrong. You just got handed a sleepy nurser. And that is screwing with your supply AND your baby's intake.
In my situation, I tried for 4 months with the supplementation and the weighing and the taking him off and on formula and the anxiety about his weight gain, and I finally said, to hell with this. I wasn't enjoying being a mother, I hated bf, and I was so consumed with whether he was starving to death everytime he cried. I put him on formula for his nutritional needs and continued to nurse him whenever he wanted (which turned out to be 2.5 years), figuring that whatever milk he got from me was a good thing.
Hopefully, things will straighten out for you. Best of luck.