Once I've eliminated scope problems for double grouping, I start looking for to a bedding problem. There might be two slightly different ways the rifle is sitting in the bedding. Haven't seen it happen with well bedded rifles but have seen it happen with un-bedded Tikkas that finally shoot the bedding a tad loose and have seen it with a Ruger a gunsmith bedded way too tight for me--was very hard to separate the action from the bedding and that gun would double group. When I rebedded it the issue went away.
