* Weather forecasts stay moderate for eastern half of U.S. * Strong storage builds, high production also weigh * Coming up: Baker Hughes rig data, CFTC trade data Friday NEW YORK, June 14 (Reuters) - U.S. natural gas futures were lower on Friday after climbing in the two previous sessions, pressured by a cooler trend in U.S. weather forecasts that should allow homeowners and businesses to turn down their air conditioners. Gas prices have been struggling for the last few weeks in the face of fairly mild late-spring weather. The front-month gas futures contract is down about 1.7 percent so far this week following a nearly 10 percent drop in the previous two weeks. With no extreme heat forecast for at least the next two weeks in key population centers of the Midwest and East, few traders expect much upside, particularly with more hefty storage builds expected in coming weeks and production still flowing at or near a record high. At 10 a.m. EDT (1400 GMT), front-month gas futures on the New York Mercantile Exchange were down 5 cents, or 1.3 percent, at $3.764 per million British thermal units after trading between $3.758 and $3.831. The front month briefly dipped to a three-month low of $3.71 on Wednesday. Early cash quotes for weekend delivery at Henry Hub , the benchmark supply point in Louisiana, were up 4 cents at $3.77 on light volume of about 415 million cubic feet. Early Hub differentials firmed to about 2 cents under NYMEX, from a 10-cent discount on Thursday. Prices on Transco pipeline at the New York citygate fell 8 cents to $3.64 on the mild late-week outlook, but volume was very light at about 18 mmcf. Many traders viewed Thursday's report of an inventory build of 95 billion cubic feet last week as neutral for prices, noting it was in line with the Reuters poll estimate of 96 bcf. But some saw it as bearish, coming in well above the five-year average increase for that week of 84 bcf. Early injection estimates for next week's Energy Information Administration storage report range from 83 bcf to 95 bcf, versus a 63-bcf build during the same week last year and a five-year average rise for that week of 80 bcf. The EIA's Thursday report showed total domestic gas inventories rose last week to 2.347 trillion cubic feet, 587 bcf, or 20 percent, below last year's record highs at that time, and 58 bcf, or just 2 percent, below the five-year average for that week. Except for some modest heat in Texas and parts of the Southwest, Commodity Weather Group expects temperatures for the eastern half of the nation to remain near seasonal for the next two weeks.