LOTR: Why Didn't The Men Of Rohan Notice Their King's Sickness?

gamerant.com:

One of the most central themes in Lord of the Rings: The Two Towers is the incarceration of King Theoden, into a weakened and feeble state where he is easily manipulated by the duplicitous Grima Wormtongue, and easily controlled by the evil powers of Saruman. It is a very clever tactic of the white wizard to control the kingdom of Rohan, which is on the bordering land to his tower in Isengard, which furthers his reach and his attempt to find the ring. Whilst Theoden is trapped in this terrible malady, Saruman’s Uruk-hai destroy villages across Rohan, stealing food, weapons and supplies, as well as scouting for the dark object that would give Saruman the ultimate dominion he desires.

This is also a clever part of a much larger plan of Sauron himself, for his aim is to let Saruman get the ring, and watch the kingdoms of Isengard, Rohan and Gondor destroy one another in their own folly. He is aware of Saruman’s plan to obtain the ring and control Gondor, but this all suits him and his bigger picture. He knows that even if Saruman did get a hold of the ring, it would still find it’s way back to Sauron anyway. After all, the ring ‘has no other master.’ But fans have always questioned why the men of Rohan don’t seem to notice the spell that their king is under, despite it being so obvious to the surrounding nations.

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There are only three people within the kingdom who seem to have an inkling that all is not as it should be with Theoden. These are Grima himself, who filled the king's mind with poison in the first place; and Eomer and Eowyn, the king's nephew and niece. Even though the two can tell that something is wrong, they have no idea what, and no idea how to stop