Both centile charts and BMI can be tricky, particularly in children. They are broadly useful, as in general terms, height and weight should track roughly together as they grow, but they don’t take into account body composition.
They are useful as we have become more and more used to seeing overweight children. When you look at the ‘chubby’ children of my youth, they look normal now.
Being 98th centile doesn’t mean you are very overweight. It just means that (out of 100 normal individuals, you would expect 2 to be heavier than you). I can’t see that you have referred to his height centile, so apologies if I have missed that, but if he is also on the 98th centile for height, then his weight is as you would expect.
As an example, I am 5 foot 2. My friend is over 6 foot. Being on the 98th centile for weight would make me morbidly obese but it would be normal for her.
(There is a slight caveat in children that overweight children tend to grow more generally, so are often also a bit taller than would be expected from parental height)
However, higher weight centile than height or increased BMI doesn’t always mean too fat. My daughter does about 16-20 hours of organised extra-curricular exercise on top of whatever she does at school, with the family and practising her activities outside training. This year, she has significantly changed in physical shape to have noticeable musculature and looks much much leaner. Her ribs and vertebrae are clearly visible. She does not have a six pack, but you can start seeing her abs. She is stronger, fitter, faster and can go further and higher. She has tracked her same height centile, but her weight centile has increased by nearly 2 centiles. In comparison, when her weight centile was less than her height, she did have a little roll of abdominal fat. Her strength, stamina and speed were only just above average. She just seems to have packed on muscle. She is still wearing clothes smaller than her chronological age, except the girth of her quadriceps now makes skinny trousers difficult.
So both measures of growth need to be interpreted in the context of the individual child.
You say that your boy has always been dense rather than fat. Could the paediatrician’s concern be because he remembers that he did not have excess fat last year to explain his weight, and that it was muscle? And therefore he didn’t consider him as having weight to “grow into”? Which therefore has promoted the comment about his lack of increase in weight. His concern may also have nothing to do with his weight, but from a nutritional basis, and he was trying to give well-meaning if a little cackhanded advice, as usually children will eat breakfast, and sometimes find concentration difficult if they don’t. Which might not apply to your son.