I have a couple of Illinois-made rifles with a cheekpiece on both sides. One is by Noel B. Devol, Marshall, Illinois (Wabash Valley). It's a long barreled halfstock, with a hand-forged barrel. The other one is also a halfstock, by Mills & Thompson, who worked at Plum River, Jo Daviess County, around 1850. It is stocked in ash, and has all hand-forged iron mountings. I have also seen a fullstock by John Cradock, Springfield, Illinois, with a cheekpiece on both sides. It dates from the 1840's.
I don't think this feature is at all regional. It went on everywhere.