The memorial service was live streamed on Scottish Rugby's website and the audio was also relayed to about 1,000 members of the public at the Greenyards rugby ground of Melrose Rugby Club.
Before the ceremony, Weir's wife, Kathy, thanked people for their support in the two weeks since he died.
"As a family, we have been overwhelmed by the many messages we have received from all over the world," she said in a statement.
"They have brought great comfort to me and the boys.
"We really appreciate people taking the time to share their own memories of Doddie and let us know we are in their thoughts."
Before the ceremony, Weir's wife, Kathy, thanked people for their support in the two weeks since he died.
"As a family, we have been overwhelmed by the many messages we have received from all over the world," she said in a statement.
"They have brought great comfort to me and the boys.
"We really appreciate people taking the time to share their own memories of Doddie and let us know we are in their thoughts."
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