With a gasp Frodo cast himself on the ground. Sam sat by him. To his surprise he felt tired but lighter, and his head seemed clear again. No more debates disturbed his mind. He knew all the arguments of despair and would not listen to them. His will was set, and only death would break it. He felt no longer either desire or need of sleep, but rather of watchfulness. He knew that all the hazards and perils were now drawing together to a point: the next day would be a day of doom, the day of final effort or disaster, the last gasp.

Sam looked at him and wept in his heart, but no tears came to his dry and stinging eyes. ‘I said I’d carry him, if it broke my back,’ he muttered, ‘and I will!’
‘Come, Mr. Frodo!’ he cried. ‘I can’t carry it for you, but I can carry you and it as well. So up you get! Come on, Mr. Frodo dear! Sam will give you a ride. Just tell him where to go, and he’ll go.’
As Frodo clung upon his back, arms loosely about his neck, legs clasped firmly under his arms, Sam staggered to his feet; and then to his amazement he felt the burden light. He had feared that he would have barely strength to lift his master alone, and beyond that he had expected to share in the dreadful dragging weight of the accursed Ring. But it was not so. Whether because Frodo was so worn by his long pains, wound of knife, and venomous sting, and sorrow, fear, and homeless wandering, or because some gift of final strength was given to him, Sam lifted Frodo with no more difficulty than if he were carrying a hobbit-child pig-a-back in some romp on the lawns or hayfields of the Shire. He took a deep breath and started off.

Sam drew a deep breath. There was a path, but how he was to get up the slope to it he did not know. First he must ease his aching back. He lay flat beside Frodo for a while. Neither spoke. Slowly the light grew. Suddenly a sense of urgency which he did not understand came to Sam. It was almost as if he had been called: ‘Now, now, or it will be too late!’ He braced himself and got up. Frodo also seemed to have felt the call. He struggled to his knees.
‘I’ll crawl, Sam,’ he gasped.
So foot by foot, like small grey insects, they crept up the slope. They came to the path and found that it was broad, paved with broken rubble and beaten ash. Frodo clambered on to it, and then moved as if by some compulsion he turned slowly to face the East. Far off the shadows of Sauron hung; but torn by some gust of wind out of the world, or else moved by some great disquiet within, the mantling clouds swirled, and for a moment drew aside; and then he saw, rising black, blacker and darker than the vast shades amid which it stood, the cruel pinnacles and iron crown of the topmost tower of Barad-dûr. One moment only it stared out, but as from some great window immeasurably high there stabbed northward a flame of red, the flicker of a piercing Eye; and then the shadows were furled again and the terrible vision was removed. The Eye was not turned to them: it was gazing north to where the Captains of the West stood at bay, and thither all its malice was now bent, as the Power moved to strike its deadly blow; but Frodo at that dreadful glimpse fell as one stricken mortally. His hand sought the chain about his neck.
Sam knelt by him. Faint, almost inaudibly, he heard Frodo whispering: ‘Help me, Sam! Help me, Sam! Hold my hand! I can’t stop it.’ Sam took his master’s hands and laid them together, palm to palm, and kissed them; and then he held them gently between his own. The thought came suddenly to him: ‘He’s spotted us! It’s all up, or it soon will be. Now, Sam Gamgee, this is the end of ends.’

J. If until now it could be argued that Sam’s emotional relationship to Frodo was more “wife” than lover, what does it mean that he is now apparently Frodo’s “dad”, not “mom”?

Never heard of the "wife" relationship in this context before. The distinction between "wife" and "lover" says a lot about conjugal expectations, doesn't it?

I've always tended to think of reciprocal parental relationships between the two of them - Frodo "fathers" Sam (with advice and encouragement), Sam "mothers" Frodo (with food and care). Maybe as time has gone on, Sam has become both parents, and the ever more helpless Frodo has become the child.

"I am going with him, if he climbs to the Moon; and if any of those Black Riders try to stop him, they’ll have Sam Gamgee to reckon with, I said." (Three's Company)

"I said to myself: 'dreaming again, Sam Gamgee,' I said." (The Great River)

"Plain as a pikestaff it is, but it’s no good Sam Gamgee putting in his spoke just now." (The Breaking of the Fellowship)

"'Whoa, Sam Gamgee!' he said aloud. 'Your legs are too short, so use your head!'" (ibid)

"You’re nowt but a ninnyhammer, Sam Gamgee!"