* U.S., Brazil agencies cut Brazilian soy, corn output estimates

* Ample supplies, sluggish demand keep lid on grain prices

CHICAGO, Feb 9 (Reuters) - U.S. corn and soybean futures hovered near three-year lows on Friday as South American crop weather improved and forecasts called for plentiful supplies, but losses were limited by short covering ahead of the weekend.

Both markets posted weekly declines, with soybeans notching an eighth straight drop and corn down for the eighth time in nine weeks.

Wheat futures were higher on bargain buying and short covering, and as the U.S. dollar softened. But the market was lower in the week for the fifth time in six weeks.

Corn and soybean markets remained focused on supply and demand estimates released by the U.S. Department of Agriculture (USDA) and Brazil's Conab a day earlier.

Both reduced projections of Brazilian soybean and corn output in the light of recent drought. Consultancy Safras & Mercado also cut its Brazilian soy crop estimate on Friday.

The USDA trimmed its global corn stocks outlook in Thursday's monthly report, but raised its world soybean stocks view to an all-time high and cut its U.S. soybean export forecast.

"The (USDA) report yesterday didn't feed the bear in corn, whereas the U.S. and world stocks for soybeans went above the high trade estimates," said Mike Zuzolo, president of Global Commodity Analytics.

Rain forecast in Brazil and Argentina, which has endured a heat wave in the past week, has also tempered worries about stress to corn and soy crops.

Chicago Board of Trade (CBOT) March soybeans were down 10 cents at $11.83-1/2 per bushel, just above this week's low of $11.79-1/4, the weakest for a most-active contract since December 2020.

March corn was down 4-1/4 cents at $4.29 a bushel after hitting a contract low of $4.28-1/4. It was the lowest for a most-active contract since December 2020.

CBOT March wheat rose 8-1/4 cents to $5.96-3/4 per bushel. (Additional reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore; Editing by Sherry Jacob-Phillips, Rashmi Aich, Jane Merriman and David Gregorio)