i dont have a weak hand...
when i shoot support hand only (that would be my left hand), i use my left eye. its not right or wrong, its just what works for me. you can use whatever eye works best for you. try both techniques... and when i say try, i mean try it for a few thousand rounds.
while we are on the topic of offhand shooting; i have learned a simple method to help my accuracy greatly. for a long time i followed what most people did - and what some people advise - when shooting offhand, and that is to cant the gun inward just a bit. some people say they feel comfortable doing it this way, however i was never very accurate shooting this way. i found that if i held the gun strait up and down (like its supposed to be) i was 100% more accurate, but it was not comfortable. i'll take accuracy over comfort anyday.