Barnes entered the spring viewed as a reserve candidate. But he started in center most of last season for the Astros, who sent him and pitcher Jordan Lyles to the Rockies for center fielder Dexter Fowler.
"I think Barnes gets left out," Weiss said. "It's a really competitive situation. The guys are showing up well."
Most of the competitors can be used as leadoff men, but Stubbs has struggled at that spot and has some skills that can work lower in the order. Stubbs batted fifth Tuesday and has been used in several places this spring.
"I'm not for sure yet exactly where he fits," Weiss said. "There are a few spots. The other day I hit him second, and I thought he looked pretty comfortable in that spot."
Thomas Harding is a reporter for MLB.com. Follow him on Twitter @harding_at_mlb. This story was not subject to the approval of Major League Baseball or its clubs.