If it's any comfort, my DD was 5.66kg at 25w/5.86kg at 28w (so close enough to 6m) and tracking the 2nd centile curve. At her 12m check she was up to 8.52kg and somewhere between the 25th and 50th centile.
As you can see from that, my DD was smaller than yours at the same age and her weight obviously took off once she was more established on solids, but still being BF 4+ times a day.
I never felt that she wasn't caught up with other babies her age. The centile charts are just a range of "normal". As long as they're gaining weight, hopefully finding a curve to stay with for a while, wherever that is, and meeting their developmental milestones, most medics will be happy. Personally I'd stick with the paed being happy and not worry so much about this other person. You've seen your paed more often, he has a full picture of how LO has been over the course of the last 6 months.