Rangers beat Falkirk 3-1 in their latest encounter.
Rangers have brushed aside all comers in the Scottish Championship this season, but their last fixture against Falkirk was a tough one.
The Light Blues were being held until the final 10 minutes of the game, when Tavernier stepped up and scored a majestic free-kick, before Lee Wallace wrapped up the triumph.
And Weir said: “We would all rather win playing open, attacking football, but within the season there are going to be times where it’s going to be difficult and where we’ll have to find another way to get a result.
“I thought the players did that well – James scored a great free-kick, as he has done on a number of occasions this season, and that really helped us.
“Sometimes one of the individuals in the team have to pull out something to get us over the line, and that was the case in the last game."
Rangers have tended to avoid relying on moments of individual brilliance to get them through matches this season, as they have blown most opponents away.
However, their latest match against Falkirk is a reminder that they cannot become complacent, despite their excellent start to the campaign.
Mark Warburton's side have won nine Scottish Championship matches in a row, and currently sit nine points clear at the top of the table.
They return to action this weekend with a game against Queen of the South, and Weir feels that it could be another tough test.
“They had a lot of change in the summer, and it think it takes time for a new team to settle in," he added.
“They’re doing that now, and last time they caused us a real problem down at Palmerston, although they had a man sent off which changed the game."