Hi, OP, just wanted to offer a quick hug: it's 23 years ago but I remember that feeling of complete helplessness so strongly. 
The situation around my dd was probably a bit different as we found out later (10 years later!) that hers had been a problem with suckling and she hadn't been getting enough nutrition even though we thought she had.
But the feeling of helplessness was the same and the feeling that as her mum somehow I ought to be able to make her grow.
We ended up admitted to hospital and got very good support there. The pictures of dd from 6 months show a smiley chubby baby. In her case, there was an underlying condition (Ehlers Danlos) which has gone on to affect her in other ways, but it was not life-threatening. When it came to the eating she just needed to turn that corner and get strong enough.
Your lo has had a bit of a tough start, hopefully he will turn the corner very soon.
Our youngest was born at a similar time and weighed slightly less; he is both tall and strong, works long shifts and does weight-lifting when he's not out running.
Fingers crossed for turning that corner, OP!