Something is keeping Henry agitated, because three weeks usually is enough time for a cat to get used to the smells and rhythms of his new home. As someone said down there, knowing the background of Henry would probably help you determine if he's afraid if something in particular.
As for right now, I suggest you spend time just sitting in the room where he's hiding, and talking softly to him. He needs to get used to the sound of your voice and the sensation of you being near. Bring him tempting foods like a bit of cheese or ham or something, so he associates you with good things. Even if he won't take it from your hand, the smell will tell him it's good.
It seems you know that it's not normal for a cat to be on high alert all the time--it will wear down his health just as it would do to a human. If you have screened windows, maybe leaving them open where he can smell the outside will make him feel more soothed. Set up a place where he can hide and feel safe--if that's under your bed, then let him hide there whenever he wants. Some cats are just painfully shy, and I think it could take as long as half a year for him to realize you mean him no harm.
Send him nice thoughts, and always be peaceful when dealing with him, because cats are very sensitive to moods. If you're agitated at his fear, he will know, and it might just make it worse.
An outside cat is not used to walking under ceilings and having spaces around them during the day--they usually curl up and sleep--he could be a very nocturnal cat who is upset at the daytime activity. If you can keep him calm during the day, or safely in a bedroom where nothing will scare him, he might realize that the day won't kill him.
Most of all, be patient with him, because it's hard to adjust to a home where you feel unwelcome (for whatever reason). When we got a second cat, our first was very hostile. She had not been raised with other cats and didn't understand cat etiquette or the smells that other cats have. It took her a very long time to stop hissing and smacking him, but now they cohabitate rather well (two years later).

GOLLY you're incredible with the detailed answers and the precise solutions! Thank you so much!

People have been coming to me for advice so long, I might as well do this all in one spot. I watch a lot of unfathomable Japanese TV and drink a lot of coffee. I'm a freshly-hatched Illustration major, formerly trapped & dying in the American South, now busily teaching phrases to all of Nagoya Japan. I'm always on the lookout for more video games and sushi.
I have lots of interesting pets. Wanna see my beetle?

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