Per Rix (LIV), probably from Proto-Indo-European*gʰrebh₂-, which allows for Winter's law and also accounts for the Sanskrit -(b)h- (but still doesn't account for the Germanic forms, which are supposed to derive from a different root *gʰrebʰ-).
Chakavian Lua error in Module:parameters at line 360: Parameter 1 should be a valid language or etymology language code; the value "Vrgada" is not valid. See WT:LOL and WT:LOL/E.: grȁbiti
Chakavian Lua error in Module:parameters at line 360: Parameter 1 should be a valid language or etymology language code; the value "Orbanići" is not valid. See WT:LOL and WT:LOL/E.: grȁbit
Please see Module:checkparams for help with this warning.Chernykh, P. Ja. (1993) “гра́бить”, in Историко-этимологический словарь русского языка [Historical-Etymological Dictionary of the Russian Language] (in Russian), 3rd edition, Moscow: Russian Lang., →ISBN, pages 210–211
Vasmer, Max (1964–1973) “гра́бить”, in Oleg Trubachyov, transl., Этимологический словарь русского языка [Etymological Dictionary of the Russian Language] (in Russian), Moscow: Progress
Trubachyov, Oleg, editor (1980), “*grabiti”, in Этимологический словарь славянских языков [Etymological dictionary of Slavic languages] (in Russian), numbers 07 (*golvačь – *gyžati), Moscow: Nauka, page 97