* Oil set for weekly losses of 2-3 pct
* U.S. crude inventories falling despite rising output
* Market shifts into backwardation, suggesting tightness (Updates throughout, changes dateline, previous SINGAPORE)
AMSTERDAM, Aug 18 (Reuters) - Oil prices edged higher on Friday, with investors offered some encouragement from data hinting that oversupply was easing steadily and a weaker dollar.
But prices were still on track to close the week 2 to 3 percent lower after concerns about weaker Chinese oil demand weighed earlier in the week.
At 0935 GMT, benchmark Brent crude futures were up 7 cents at $51.10 a barrel on the day but still about 2 percent lower on the week.
U.S. West Texas Intermediate (WTI) crude futures were up 16 cents at $47.25 a barrel, although they were also set to end the week more than 3 percent lower.
"Falling U.S. commercial stocks are supportive and I also believe that high U.S. product demand, and gasoline demand in particular, is helping too," Tamas Varga, senior analyst at London brokerage PVM Oil Associates, said of Friday's move up.
He also said a weaker dollar was bullish for oil prices as equity markets piled pressure on the greenback.
The Brent forward curve has moved from contango into backwardation, where prices for immediate delivery are higher than those for the three future months. A backwardated market is considered a bullish sign for prices since it indicates demand is outpacing supply.
Signs of supply tightness have started appearing in the United States, the world's biggest oil consumer.
Despite a 13 percent jump in production <C-OUT-T-EIA> since mid-2016 to 9.5 million bpd, the country's commercial crude inventories <C-STK-T-EIA> have fallen 13 percent from their March records to below 2016 levels.
(Additional reporting by Henning Gloystein; Editing by Edmund Blair)