* Dollar drops on bond market gyrations, lifts commodities * OPEC raises slightly forecast for world oil demand growth * Saudi air offensive in Yemen feeds concern over Mideast crude * EIA cuts 2016 oil demand projections * Coming Up: API US crude stockpiles data for last week at 2030GMT (Updates with settlement in Brent, paragraph 7) By Barani Krishnan NEW YORK, May 12 (Reuters) - Oil rose as much as 3 percent on Tuesday as a weak dollar lifted commodities de**minated in the currency and OPEC raised slightly its forecast for world oil demand growth. Violence in Yemen also boosted crude prices, raising concerns over the security of Middle East supplies. The dollar fell on bond market gyrations, making oil and other commodities priced in the greenback more affordable to holders of the euro and other currencies. The Organization of the Petroleum Exporting Countries tweaked its 2015 world oil demand growth forecast to 1.18 million barrels per day (bpd), above a previous estimate of 1.17 million.