Oil stayed above 129 dollars a barrel in Asian trade Wednesday, driven by concerns over tight global supplies amid strong demand, dealers said.  In morning trade, New York's main oil futures contract, light sweet crude for July delivery, was up eight cents to 129.06 dollars a barrel. The contract for June struck an all-time high of 129.60 dollars, before expiring at 129.07 dollars on Tuesday at the New York Mercantile Exchange. London's Brent crude contract for July was down four cents at 127.80 dollars a barrel, after settling at 127.84 dollars on Tuesday. It had briefly hit a new all-time high of 128.07 dollars earlier.