The cook is their brother, not their father
I know that won't be news to some of you, but I'm usually met with derision when I say he's the brother of Leatherface and the hitchhiker. It seems like everyone thinks he's the father. I say no way. Here's why:
1. The hitchhiker mentions his brother worked at the slaughterhouse. There's no way he's talking about Leatherface. I mean, can you imagine Leatherface holding down a job? Sure, I can just picture him picking out his outfit for the job interview, wondering what face he's gonna wear to make a good impression.
Now forget for a moment that Leatherface was shown working at the slaughterhouse at the beginning of the sequel to the remake (that being TCM: The Beginning, of course). That, for me, has no meaning in regard to the original TCM. In TCM: The Beginning, while at the slaughterhouse, Leatherface just seems really creepy and intimidating, but someone who could still hold it together at work (at least until he's fired, that is). In the original, Leatherface is presented as an absolute mental defective who is prone to uncontrollable homicidal outbursts. The hitchhiker couldn't have meant that Leatherface was the brother who worked at the slaughterhouse.
2. If the cook was their father, why would he refer to his father as grandpa? Admittedly, lots of parents do that when mentioning their parents to their kids, just like a dad might call his wife "mom" in front of their kids, instead of by her name. In this case, the cook calls him grandpa because he is his grandfather.
3. Okay, I probably should've led with this, but in the book "The Texas Chain Saw Massacre Companion", on page 41, both Gunnar Hansen and Jim Siedow confirm that the cook was the eldest brother.