Japan top World Cup Pool B after Saturday's thrilling 34-32 win against a vastly experienced Springboks side.
"We understood that Japan are a growing nation and they've been playing some good rugby," said fly-half Weir.
"It's not a surprise in our camp. They merited getting the victory because they put in a very good performance."
Japan's success in Brighton was their second victory at a World Cup and came against the two-time winners, with almost 900 caps between their starting XV.
When asked if Scotland are now underdogs going into Wednesday's match in Gloucester, Weir replied: "That's not for us to comment on.
"I believe we have the players in this squad to do very well in this tournament.
"I'm sure we can put Japan under pressure and score points.  I'll leave all the talk about favourites to the media.
"South Africa struggled at set-piece and at scrum time; they didn't front up as they would've liked. South African forwards like to dominate in that area and they didn't get that dominance.  That's one of the reasons for the result.
"We always knew the Japan game was going to be a huge test.  We're gearing up for a battle on Wednesday."
Scotland have won all four of their previous encounters with Japan, including World Cup pool matches in 1991 and 2003.
The most recent clash came at Murrayfield in November 2013, with Glasgow Warriors' Weir among the try-scorers in a 42-17 triumph for the hosts.
Scotland open their tournament against a side that will have three days to recover but team manager Gavin Scott does not think Japan's physical and mental effort against South Africa will have a bearing on how head coach Vern Cotter uses his replacements' bench.
"The schedule hasn't changed," said Scott. "Japan still have a tight turnaround.
"They played a really brutal game of rugby regardless of the result but I don't think the substitution policy will have changed too much. These things are never set in stone because things change in games."
Duncan Weir insists the Scotland squad were not shocked by Japan beating South Africa and says it acts as a warning ahead of Wednesday's meeting.