The 21-year-old claimed the majority of the votes online to beat the likes of Manchester City striker Jane Ross and Arsenal Ladies midfielder Kim Little to the award.
Weir was a regular for Scotland throughout 2016, helping her country to qualify for the 2017 European Championships later this year.
The Reds No.10 was also named Liverpool Ladies Supporters' Player of the Year in 2016 and won the Goal of the Season a for her stunning second strike against Doncaster Rovers Belles.
On picking up the gong, Weir said: “Winning this award is a huge honour and one that I did not expect.