How much does the PGA Wanamaker trophy weigh exactly?

44 pounds.

"AKRON, Ohio (AP) -- Padraig Harrington had to play 27 holes in the final round at Oakland Hills last year when he won the PGA Championship. Then came the hard part -- mustering enough strength to hoist the heaviest trophy among major championships. "Forty-four pounds," he said."

pga.com/pgachampionship/2009/news/heavy_080809.cfm nolonger exists

Twenty-seven pounds. The quoted article is all about the trophy being a relative lightweight in the sports world.

http://www.sbnation.com/2009/8/17/1644427/wanamaker-trophy-is-big-for-y-e

Lower part of post may explain the weight discrepancy above -- 44 pounds and 27 pounds:

The Wanamaker trophy however, announces its presence. It is by far the biggest of the major-championship trophies, standing tall (28 inches), wide (10½-inch diameter) and heavy (27 pounds).
http://sports.espn.go.com/golf/pgachampionship06/columns/story?columnist=rosaforte_tim&id=2549547

Certified appraisers at Cash4Gold have estimated that the 27-pound sterling silver Wanamaker Trophy contains roughly $5,500 worth of precious metals. This is the heaviest prize awarded at golf's four major championships - The Masters, U.S. Open, British Open and PGA Championship.

The Wanamaker trophy was donated by Rodman Wanamaker and is worth aprox $35,000. The trophy is: 27 pound (12.25 kg), 28" in height (71cm), 10.5" in diameter (26.5cm) and 27" handle to handle (68.5cm). The Wanamaker trophy is not kept by the winner of the competition. Instead, the winners receive a replica trophy which is half the size of the original.
http://golf.about.com/od/majorchampionships/f/pga-championship-trophy.htm

Both 27 and 44 pounds seem to be reported in numerous locations. There are more references to 27 than to 44. Also, the references to 27 seem to be more reliable sources to me. The PGA site for example seems like it would be the definitive answer:

"Wanamaker vowed to change that, and his luncheon resulted in formation of The PGA of America. He suggested a professional-only tournament, put up $2,500 of his own money for the prize fund, and ordered a silver cup. A man with such great vision demanded a great trophy. What he got was 28 inches high, 10-1/2 inches in diameter and 27 inches from handle to handle. It weighs 27 pounds, even without a young child on top."

pga.com/pgachampionship/2008/news/wanamaker_080308.html no longer exists

These four sites all have 27 pounds (12.25kgm):
https://thegolfnewsnet.com/golfnewsnetteam/2020/08/07/wanamaker-trophy-facts-size-weight-history-namesake-74365/
https://www.golfdigest.com/story/pga-tour-pros-trophies-the-spoils-of-victory
https://www.washingtonpost.com/news/early-lead/wp/2018/08/09/i-was-genuinely-shocked-by-the-weight-meet-the-wanamaker-trophy-golfs-burliest-prize/
https://www.golfmonthly.com/tour/uspga-championship/uspga-history-and-records/wanamaker-trophy-77980