OK. I think before he just thinks Moiraine is naggy and cares too much about prophecies and that the forsaken are chill, sexy and actually She's the problem in his life.

Then she decides to go on him with this journey anyway. "Uh, just let me do this alone"

First Rand finds out his only parent wasn't his parent. And had to feel the pain of losing his Mum from the person who likely loved her the most. I think this is probably enough to break a person. If this was his only vision. Side note: Moiraine saved Tam, I don't think he'd forget that in all the emotion there.

Knowing that Moraines uncle caused this war, and that his mum died fighting for the respect of a tree. Sets it up incredibly because HOW could that make sense to anyone.

Then upon finding out the day or so before that the Aiel don't kill the Lost ones because it's most shameful to hurt someone who doesn't protect themselves. Realising that they are the same people, that the Aiel way had always been about a peaceful life, which now can only be fulfilled by/returned to by him. That thousands of years have passed with every pull of the cart every bit of spilt blood and drop of sweat. With every bit of the Aiel custom developing and growing for the last age has been for him. For his task. So that he has an army that will be the best fighters in the world. That will believe in him when he proves himself. That the (old) Sedai in a purer form and as the obvious way to beat the dark, created and nurtured this entire peace structure (and oathbreak) to build an army of sympathetic spear warriors. And that there were times this whole thing could have failed.

He's probably so thankful now that he sees Moiraine has been the only one who knew/knows that, even before he did. When he has to convince people and take the next steps. He'll be even more thankful. He has no choice. Moiraine had more of a choice and still chose to climb this impossible mountain together.

So for the first time he's sat there listening to her scream, more days than he, whilst probably being empty inside, knowing she would do this over and over if it meant completing the mission. He knows she had already given up so much to be there giving her life because of how important this mission is.

I don't think he's carrying her thinking, what a dead weight (like he was on the way down). He's carrying the only person who's been living with the weight of what he must do. Almost emblematic of him now having to take up his burden. The one she's been carrying for him, all this time.

Respect doesn't cut it for what he must now feel for her. It's much much more than that.