Painted by artist Gerard Burns, it shows the former Scotland forward in his statement tartan suit with the Eildon Hills, near Melrose, in the background.
"My good lady said I was no oil painting ... well, I'd like to dispute that", Doddie said on Twitter.
"We are delighted to know that we have been able to help so many families over the last two years," said Weir.
"There are many challenges to living with MND and it has been my aim to help people in a similar situation to myself live as full a life as possible.
"The grant schemes are vital and we are only able to help in this way thanksto the amazing support we receive from our fundraisers and friends every day."
The painting is on public display in the great hall as of Thursday for the duration of the Six Nations Championships, and then it will move to alongside well-know Scots such as actors Alan Cumming, and Tilda Swinton.