From Black (The Surnames of Scotland, Their Origin, Meaning and History):
"Stobie It may be a form of Stobo. William Stobbe was burgess of Berwick-on-Tweed in 1318. Master Henry Stoby, clerk at Perth, 1356. Dand Stobe was tenant on the lands of the Abbey of Kelso, 1567. Henry Stobie is recorded in Dunfermline, 1587 and John Stobie had a charter of the lands of Waster Luscoir in 1605. The surname is found in Methven, 1674 and John Stobbie was merchant in Crieff, 1787. Matthew Stobie was land surveyor in Edinburgh in the beginning of the 18th century."