* Front month hit highest mark since July 2011 on Monday * Chilly weather seen continuing through April * Nuclear plant outages still above five-year average * Coming Up: Reuters natural gas storage poll on Wednesday By Joe Silha and Eileen Houlihan NEW YORK, April 16 (Reuters) - U.S. natural gas futures ended higher on Tuesday in a seesaw session with light profit-taking pressure finally overwhelmed by supportive weather forecasts that should underpin heating demand through most of April. Front futures have gained ground in eight previous weeks, climbing nearly 35 percent since mid-February as chilly late-winter weather and above-average nuclear plant outages whittled down record high inventories and tightened overall supplies. Despite the near-term chill, some traders have doubts about the upside, noting new longs piling into the gas market over the last month have driven futures open interest to record highs and could leave the market vulnerable to a sharp, profit-taking sell-off once temperatures turn milder. "Everyone's long, so there may not be that many buyers left. Sure it's cold but that's already priced in, and I don't see the impetus to drive prices up much further in the near term," a Houston-based cash trader said. Front-month gas futures on the New York Mercantile Exchange ended up 2.3 cents at $4.16 per million British thermal units after trading between $4.084 and $4.194. The front contact posted a 20-1/2-month high of $4.29 on Monday. Traders also note that gas prices are at, or near, levels that could slow demand by prompting more utilities to switch back to coal for power generation and to increase supply by tempting producers to hook up more wells. MDA Weather Services said that the six- to 10-day outlook continued to show plenty of cold, with well below normal temperatures expected for the Plains, Midwest and South, while mid-Atlantic states will see below normal readings. The West will be warm during the period. INJECTION SEASON SET FOR SLOW START The stock-building season is set to get underway, with Thursday's U.S. Energy Information Administration storage report likely to show a build of between 15 billion and 40 billion cubic feet. Stocks rose 21 bcf during the same week last year, while the five-year average rise for that week is 39 bcf. But persistent cold in April, particularly in the Midwest, is likely to keep weekly injections below average and drive overall inventories further below the five-year average. EIA data last week showed that total domestic gas inventories had fallen to 1.673 trillion cubic feet, 32 percent below last year's record highs for the period and 4 percent below average. Winter withdrawals this year totaled about 2.25 tcf, roughly 770 bcf, or 52 percent, more than last year, and 15 percent more than the normal draw during the heating season. RIG COUNT CLIMBS, WHEN WILL OUTPUT SLOW? Baker Hughes data on Friday showed the gas-directed rig count rose last week by two to 377, raising concerns that higher gas prices may be stirring more dry gas drilling. Drilling for natural gas has mostly been in decline for the past 18 months. The count is down about 60 percent since peaking in 2011 at 936 and is hovering just above the 14-year low posted two weeks ago, but so far production has not slowed much from the record high hit last year. EIA recently trimmed its estimate for domestic gas production growth in 2013, but still expects output to rise 0.3 percent from 2012's record levels.