Richard: It's likely I'm giving you information which you already have or covering things which you have looked into but here goes anyway:
1) Perhaps this couple was not married in Illinois since census info indicates both were born in New York. Their first child, "Hattie" (Harriet?) was born IL 1857 so you know they were there by roughly 1857 (if the census is correct). But census records are often wrong: what I believe is their son, Edger R., has a birthplace of IL in 1870 and 1880 but in the 1900 census, shows Wisconsin as birth place with both parents born Wisconsin. The 1870 is also interesting because it tells you that:
2)In addition to the immediate family and a couple of servants, there is an Eloise Woodruff, 33, born NY and an Emma Woodruff, 13, born IL living with them. Unfortunately, relationships are not given so one can only speculate. Was this a widowed sister to Uriah or could it be a twin sister to Helen or ?????. Furthermore, Uriah's occupation is given as attorney with respectible assests, both real and personal, so that tells me:
3) He might well have left a will but, if not, it's certainly possible there was an administration opened. It's quite possible that Helen's maiden name can be found in such documents. Personally, I would look into this angle. Deed records might also help. I believe the couple was living in their own home in 1870 but by 1880 widow Helen and son Edger were living in what appears to be a multi-family building (apartment maybe). That indicates that she might have sold the home after Uriah's death in 1876. Such a sale might also reveal her maiden name.
4) I assume that your info on Helen's death comes from the VERY brief notice in the "Chicago Tribune", right?
5) Uriah's death notice was published and states: "Hawley, Nov. 5, at 2 o'clock a.m. U. R. Hawley. The funeral will take place from his late residence, 271 Warren ave. near Robey street, at 11 o'clock a.m. on Wed., Nov. 8, by carriage to Rosehill. Friends are invited." [Chicago Tribune, 7 Nov. 1876, pg. 8]
6) I believe son Edgar R.'s obit also appeared in the "Tribune", wasn't he a physician, married to Helen Schmelt/Scumelt (unsure of spelling, can't read my notes)?
If you don't have obit copies and want them, just let me know. Just some suggestions and thoughts. Rick