Dear Dave in Illinois:
I don't have much information on my Hedebrinks other than the direct line. A distant cousin had some research done in Germany over 20 years ago, and he was able to track the line back to the late 17th century. As for the spelling, everything indicates that it was Hetebrink or Hedebrings.
This is the lineage that I have:
1. Rennig Hetebrink, born 9 Jan 1689/90 in Eitzendorf, died 18 Sept 1726 in Eitzendorf. He married Beke Bultmann 22 Oct 1703 in Eitzendorf.
2. Their son was Johann Jurgen Hetebrink, born 24 Aug 1704 in Eitzendorf, died 29 Aug 1736 in Eitzendorf. He married Anna Ilse Hopmann (born Sept 1706 in Martfeld, died 14 March 1785 in Eitzendorf) on 23 Nov 1729 in Eitzendorf.
3. Their daughter was Rebecka Elisabeth Hedebrings, born 8 May 1733 in Eitzendorf, died 19 Aug 1803 in Eitzendorf. On 10 Oct 1760 in Eitzendorf, she married Friedrich Ludolf Grieme, who was born in Steinborn.
4. Their son, Hermann Hinrich Friedrich Grieme (my gggg-grandfather) was born on 11 Oct 1771 in Eitzendorf, and died on 7 Dec 1827 in Martfeld. He married Anna Dorothe Geils (born 23 July 1776 in Martfeld, died 13 June 1844 in Martfeld) on 1 June 1804 in Martfeld.
Since the spelling is different, this may not be your family at all. However, I included some of the names, dates, and places just in case they "fit" with your family.
Kathy in Ohio
Volga-German: Feit, Fromm, Ehrlich, Schmunk, Haffner, Winter, Blehm, Seibert
Germany/Netherlands: Bartels, Herzberg, Herzog, Rippe, Wagoner, Sunderman, Grieme, Busing, Hedebrinks, Moening, Goecker, Ralker
New England/England: Partridge, Brock, Woodruff, Lewis, Wright, Woodward, Rose, Tracy, Wyman, Stanley, Dennis, Savage
Pennsylvania/Ohio: Stahlman, Callen, Armstrong, Paul, McCrory, Wallace, Daniels, Goodenough, Davidson, Snodgrass, Burris, Brady, Phillips