The Manchester City midfielder played the full 90 minutes in Rennes, as Shelley Kerr’s side suffered a second consecutive defeat, which leaves them bottom of the group after two games.
Mana Iwabuchi fired home from 20-yards before Yuika Sugasawa scored a penalty, to give Japan a deserved lead at half-time and though Scotland rallied, Lana Clelland’s 89th minute strike came too late to inspire a fight back.
Having lost by the same margin in their tournament opener against England, Weir's final group game against Argentina is a must win if Scotland are to have a chance of qualifying as one of the four best ranked third-placed teams.
They were giving away 13 places in the world rankings and Japan’s superiority showed in a first half.
The 2011 world champions controlled possession to carve the Scot's open on several occasions and capitalised on Rachel Corsie's tame clearance to break the deadlock.
Iwabuchi was teed up on the edge of the area and her fierce strike went high into the centre of the net.
Corsie, the Scottish captain, then made the slightest of contact with Sugasawa to concede her side’s second penalty of the tournament and the Japan striker duly despatched the spot-kick into the bottom right corner 10 minutes before half-time.
Japan also hit the post before the break, but Scotland and Weir got on the ball more in the second period.
The City midfielder unleashed an effort from distance as the trailing side played with more attacking intent and sent in a teasing free-kick, which Erin Cuthbert turned onto the post.
As the clock ticked down, Scotland had their own claims for a penalty waved away after Risa Shimizu looked to have handled in the area, before Clelland struck.
Capitalising on Nana Ichise’s loose pass, the Fiorentina striker arrowed an 18-yard effort into the top corner to net a goal which could still prove vital to the ranking of third-placed teams.
Weir and Scotland now face a crucial final group stage game against Argentina, which takes place at 8pm (BST) on Wednesday 19 June.