is Jon tall like Rhaegar?
Well, how tall was Rhaegar? There’s very few canon descriptions of peoples heights (I only remember Robert being specified as 6′6″, Gregor as almost eight feet, perhaps some others as well) so it’s really just a matter of picking through book descriptions to figure out how tall everyone is relative to each other.
I’ve always assumed that Rhaegar was over six feet tall, but no taller than 6′6″. That made sense to me because of his opponent on the Trident, Robert, and I can’t imagine that Rhaegar could be much shorter than him. He was also noted as being taller than Viserys, but again, I’m not really sure how tall Viserys was. Targaryen men are generally pretty tall, tho.
We also do not have a good description on Jon’s height, but if I had to guess, I’d say he is around the same height as Robb. Catelyn describes Robb as “tall” several times. In AGoT, at the age of fifteen, she described him as being “nearly as tall as she was” and that she prayed he would “grow as tall as his father”, who was probably in the neighborhood of 5′11-6′3″ himself (he was shorter than Robert). Catelyn herself I believe is tall, but not unusually so (not like Brienne or Dacey, for example; my guess is 5′8″). Since Catelyn tends to call Robb “tall” in the later books, I’ve assumed that he put on some inches and surpassed his mother, but I don’t think he had a chance to grow any taller than 6′0″, if he even was that tall. I’d put him at 5′11″/5′10″ max.
Jon himself isn’t described as exceptionally tall by anyone, really. There are people taller than him. Stannis, for example:
A big man, Stannis Baratheon towered over Jon, but he was so gaunt that he looked ten years older than he was.
All Baratheon men are tall, though, and I’d imagine Stannis was at least 6′3″, with the maximum being 6′6″, as I assume Robert was the biggest and tallest out of all of his brothers.
SO. After all of this hyper-analyzing, where does this put Jon Snow? The speculative timeline tells us that Jon Snow was seventeen by the end of ADWD. Using all of these numbers, I’d wager he’s between 5′10″ to maybe, maybe six feet. My money’s on him being just under 6′0″, though, and thus shorter than Rhaegar.
As an aside, Lyanna herself was likely no more than 5′5″, if the story of the KoLT is anything to go off of. The knight was described as being “short of stature”. Even if it was Howland Reed in the armor (it’s not ofc), he was probably around 5′5″ himself, seeing as his children, including sixteen year old Meera, are described as being “scarcely taller” than a nine year old Bran.
In summary: Baratheons are tall, crannogmen are tiny, Lyanna was a lot shorter than Rhaegar, and Jon’s height likely falls somewhere in between his parents’.