The two politicians, along with Mr Johnson’s wife Carrie, all received fixed penalty notices for attending a birthday gathering for the Prime Minister at 10 Downing Street.
Ms Tweed said: "Boris Johnson and Rishi Sunak’s positions are untenable, they simply must resign.
"The Prime Minister repeatedly misled Parliament, lied and took the people of Scotland for fools.
"How can we accept a prime minister who has been seen laughing about breaching the same laws we were all following to keep our families safe.
“Douglas Ross and the Scottish Tories are no better as they appear to be unable or unwilling to grow a backbone and call on Boris Johnson to resign.
"The fact of the matter is, Johnson and Sunak have overseen one of the biggest lockdown breaches that has led to the Metropolitan Police issuing a staggering number of fines for rule-breaking.
"The Prime Minister and Chancellor of the Exchequer have insulted people across Stirling who faithfully followed the rules that they set – even when that meant the heartbreak of not being present for the births, marriages or the deaths of loved ones.
"There simply cannot be one rule for the Tories and another for the rest of us.
"If Johnson and Sunak have a shred of dignity they will finally do the right thing and resign now.”