Hi,Katheryn Rose - It sounds as if you are on the right track. My husband's mother was an Achey. The name has come to be spelled and pronounced in other ways by different lines of the family. My research tells me that the name Achey means your ancestors are people who came from Aachen, Germany. There are at least 2 towns with that name in Germany. One of those towns is very close to France, so some Acheys became French and married French spouses. Normandy, a part of France, and Holland are other places that the Acheys could have emigrated.
My husband's mother grew up in the state of Washington after some of the the German Acheys living in Pennsylvania gradually moved west. "Pennslyvania Dutch" is what the Germans were called because they spoke "Deutsche" and called themselves that which meant German in their language. So your Achey's may never have been in Holland, but still have been called "Dutch".
So you have some good information, it just needs to be explained by a little history. You are right that most of the Acheys seem to have come into the United Sates through Pennsylvania. That was true of many Germans in the late 1600s and all through the 1700s. Then some stayed and some moved to other places such as Ohio and North Carolina that were popular with the Germans.
My husbands Achey family went the Ohio route before later generations got to Washinton. My own German ancestors went to North Carolina.
I'll try to copy this message to your personal email.