* Prices weighed by falling grains markets, weaker-than-expected U.S. retail data

* Fiber sees first weekly gain as steep price drop sparks mill buying

* U.S. government's monthly forecast reinforces bearish expectations

* Speculators cut cotton net long to lowest since late January -CFTC

NEW YORK, Sept 13 (Reuters) - ICE cotton eased on Friday under pressure from falling commodities markets and weak U.S. retail sales, though they saw their first weekly gain in four weeks as a dip to three-month lows renewed demand.

The most-active December cotton contract on ICE Futures U.S. closed down 0.29 cent, or 0.3 percent, to settle at 84.46 cents per lb.

U.S. retail sales rose less than expected in August, sparking worry over the economy's momentum and sluggish demand for consumer products, including apparel.

Grains led the declines in commodities markets, as the entire Thomson Reuters-Jefferies CRB benchmark commodity index fell. The declines weighed on fiber, which competes with the more lucrative grains crops for acreage in the United States.

"A lot of the commodities are down. There wasn't much to keep cotton higher today," said Sharon Johnson, a cotton specialist with KCG Futures in Atlanta.

The second-month prices gained 1.5 percent since last week's close, up for the first time in four weeks as prices recovered from three-month lows.

The December contract found support near the 200-day moving average of 84 cents. A tumble of some 10 percent from last month's peak of 93.72 cents a lb has sparked renewed interest from mills, seen in this week's U.S. government export data.

"The market is now looking toward demand. China bought another round of cotton last week. That's the floor underpinning the market," said Spencer Patton, founder and chief investment officer of Steel Vine Investment in Chicago.

The speculators who piled into the fiber market and drove last month's run-up have since exited in droves. They cut their position for a third straight week in the most recent reporting period, dropping it to the lowest level since January, weekly U.S. government data showed on Friday.

China began stockpiling cotton this week, boosting prices, as it eased merchants' worry over demand from the top consumer.

The stockpiling program Beijing launched in 2011 has driven voracious demand for lower-priced, foreign cotton.

Even so, a U.S. Department of Agriculture (USDA) report this week sparked concern over falling demand for U.S. cotton, as the government reduced its outlook for exports by 200,000 bales in crop year that ends July 31.

The monthly U.S. government forecast reinforced bearish expectations for a cotton market where global supplies continue to outstrip demand, leaving expected inventories at a record of nearly 95 million bales by the end of 2013/14.

(Reporting by Chris Prentice; editing by Andrew Hay)