* Dollar rallies to 3-week high versus yen as stocks rally

* Euro, sterling hurt by disappointing economic data

* US manufacturing index lowest since 1980

(Recasts, adds comments, updates prices, changes byline)

By Wanfeng Zhou

NEW YORK, Jan 2 (Reuters) - The U.S. dollar rallied to a three-week high against the yen on the first trading day of 2009 on Friday after a strong performance on Wall Street encouraged risk appetite.

The dollar also gained versus the euro, after data showed deepening recession in the euro zone and as traders deemed the euro's rapid advance last month was overdone. Thin holiday trading volumes may have exacerbated currency moves, analysts said.

"The rise in stocks here in the U.S. and globally, at least for now, has increased risk appetite," said Omer Esiner, senior market analyst at Ruesch International in Washington. "Dollar/yen has benefited from that, particularly in holiday thin trade."

Risk aversion has seen the low-yielding yen soaring over the past year, with the dollar losing more than 18 percent versus the Japanese unit, its worst annual performance since 1987. An improvement in risk appetite tends to be associated with yen-selling.