Maybe it's an old enemy who has somehow survived and is now more powerful. They could be seeking revenge on Captain America for past defeats. For example, Red Skull could have found a new way to return and cause trouble.
The Night King could be a great antagonist. His army of the dead and his own powerful magic would pose a huge threat to Captain America. Cap's used to fighting human foes, but the Night King is something entirely different.
One possibility is that he wakes up and discovers new allies. The story could then revolve around him building relationships with these new characters while still holding onto his old values. He may also have to deal with the fact that the world has moved on without him and find his new place in it.
The main antagonist could be a powerful sorcerer. As I mentioned before, in the context of a magical curse causing the weight gain. This sorcerer could have his own motives, like trying to take over the world by first weakening the Avengers' most iconic figure. He could use his dark magic to mess with Captain America's body and make him gain weight, and then use this as a distraction while he executes the rest of his evil plan.
It could be a rogue Amazon who disagrees with the idea of an outsider like Captain America being on Themyscira. She might see him as a threat to their way of life and try to drive him out, or even worse, harm him.
Well, in some fanfics, they might make Captain America seem like a jerk to create an interesting plot twist. Maybe they show him being overly self - righteous or making bad decisions that go against his usual heroic image.
Thanos could still be a great antagonist even in a fanfic. He could come back with a new plan to obtain the Infinity Stones again. His powerful and menacing presence would create a high - stakes situation for Captain Marvel and the Avengers to face.
An alien race with a grudge against the Republic could also be the main antagonist. They might target Rex specifically because of his strategic importance and his role in leading many successful missions against them in the past. His death at their hands would be a major blow to the Republic's morale.
He could also meet Odin. Odin might view Captain America as an interesting mortal from Midgard and might have some words of wisdom or a task for him to complete during his stay in Asgard.
Captain America could fit in by sharing his sense of morality and leadership. In the TOS universe, which often deals with complex moral and ethical dilemmas, his straightforward and noble values could provide a different perspective. He might be involved in diplomatic missions, using his charisma and integrity to negotiate with alien races. Also, his military experience could be applied to strategic planning during the crew's missions.
There's also 'Captain America: Reborn'. In this fanfic, Steve Rogers has to face a new threat that is specifically targeting his ideals. It's a great read as it explores his unwavering beliefs and how he inspires those around him even in the face of seemingly insurmountable odds. It also has some unique interpretations of his powers and abilities.