Yamato might show his concern by constantly checking on Naruto's condition. He could be seen sitting by Naruto's bedside, feeling his forehead for fever regularly.
Maybe in the fanfiction, there's a new enemy that targets the old - timers like Naruto and Yamato because of their past achievements. They are forced to come out of retirement and use their rusty but still formidable skills to defend themselves and the village. They might also have to train some inexperienced shinobi along the way to help in the fight.
In the fanfiction, old man Naruto might be facing some sort of threat to the village again. He calls on Yamato, his old comrade, to help him. Together, they plan strategies and use their combined skills, with Naruto's nine - tails power (albeit in a more controlled and aged - related way) and Yamato's wood - style jutsu to protect the village one more time.
Yamato might first be a bit shocked. But then he'd probably try to calm Naruto down. He could use his wood - style jutsu to create a peaceful environment, like making a small forest around them to soothe Naruto.
Naruto might be in awe of the battleship Yamato at first. He could use his chakra to enhance the ship's speed or power in some way. For example, he could transfer some of his chakra to the engines to make it move faster.
Yamato's wood - style jutsu could be seen as a form of nature - based magic in the Devil May Cry world. He could use it to create barriers against demons or even trap them, much like how Dante uses his devil arms to fight. His ability to sense chakra might also translate to sensing demonic energy, allowing him to detect hidden demons.
Yamato might first try to use his calm and steady presence to soothe Naruto. He could place a hand on Naruto's shoulder and speak in a gentle voice, telling him to take deep breaths.
Weiss, with her more refined upbringing, could initially be a bit shocked by the differences in the Yamato's world but would soon start to find ways to use her skills. She might help with strategic planning, using her knowledge from Beacon Academy.
A simple way is to have Yamato train Naruto in katana - wielding techniques. Since Yamato is a skilled ninja, he could teach Naruto how to handle a katana, which Naruto might initially resist as he's more used to his own combat style. But as he learns, he discovers new ways to combine his ninjutsu with katana - based attacks.