The Scottish international, who his agent claims has attracted admiring glances from Manchester United, was a comfortable winner with 1,165 votes.
As less than 3,000 entries were recorded for The Toffees, Weir was the only player to reach four figures.
Canadian international striker Tomasz Radzinski may not have had the perfect first season in The Premiership, but he will be pleased to have finished in second place.
Nine votes behind the former Anderlecht man in third was popular centre back Alan Stubbs.
David Unsworth was fourth, ahead of goalkeeper Steve Simonsen and promising full back Gary Naysmith.
Result:
1.Weir, 2.Radzinski, 3.Stubbs, 4.Unsworth, 5.Simonsen, 6.Naysmith.
