is it possible that melantha blackwood and betha blackwood were sisters?
Possible? Sure. Probable? Well … hard to say, but I think it’s not unlikely. We actually have a pretty accurate read on Betha Blackwood’s age: Yandel tells us that the Blackwood maid married Prince Aegon in 220 AC, when she was 19 and he was 20. Therefore, Lady Betha Blackwood had to have been born in or around 201 AC.
Melantha, however, is harder to get a read on: we know she was married to Lord Willam Stark as one of his eventual two wives, we know that she bore him two children, and we know that Willam himself died in 226 AC at Long Lake, fighting the King-Beyond-the-Wall Raymun Redbeard. That’s not much, but I think with a little (or maybe a lot of) guesswork we can pierce together a rough estimate of Melantha’s age.
Start with Rickard Stark. Pycelle notes to Eddard that the summer of King Maekar’s reign, which occurred before Rickard’s birth, lasted seven years, followed by a quick autumn and brutal winter; moreover, we know from Yandel that there was a winter that lasted from 230 to 236 AC. So if summer lasted from, say, 222 to 229 AC, then autumn from 229 to 230 AC, then winter, I think Rickard might have been born in the midst of that winter (to fit with Pycelle noting that Maekar’s summer was forgotten before Rickard’s birth; after five years of winter, I might expect people to have forgotten about the longer summer). If Rickard was indeed born in roughly 235 AC, then I think it’s a fair guess that Papa Edwyle Stark was born in roughly 210-215 AC. I think a later date on that scale is more likely: William died in 226, and while it’s possible Edwyle succeeded automatically, I think it makes a little more sense that Uncle Artos “the Implacable”, who had slain Raymun Redbeard and ordered the Night’s Watch around after the battle, ruled as his nephew’s regent until Edwyle came of age - hence his getting a statue in the crypts of Winterfell.
ALL of this is to say, if Edwyle was born ~215 AC, then we might expect that Melantha might have been around 16 or 17 when he was born, on the younger end (neither too young - there was no pressure for Willam to marry a child bride, with the surplus of Starks in his generation and memory of recent family infighting - nor too old as to arouse comment, like Fat Walda’s cheerful disdain of Fair Walda’s unmarried state at 19). That would place her own birth in the 198 AC area, give or take a few years for Edwyle’s age and her own birth relative to that. Naturally, if she were born in or around 198 AC, that would make her perfectly of an age to be an elder sister to Lady Betha.
Obviously, this is a good handful of guesses and assumptions re: age. Melantha could have been older or younger than I paint her here, and even if her age is correct, that doesn’t necessarily mean she was a sister and not, say, a cousin (hell, the future Queen Victoria was only three days older than her first cousin, the eventual King George V of Hanover). That said, I think it’s a perfectly acceptable belief with the current state of information to say that Melantha was Betha’s sister (interestingly enough, that would make Rickard and his murderer Aerys second cousins, and Rhaegar a third cousin of Lyanna).