The fiercely private couple, who scooped £161 million in 2011, say they have had to put up with "downright nasty" comments over the years, but have now had enough after their latest £1m donation to the pro-independence group provoked strong criticism.
In a letter to The Herald, the pair responded to claims they have been targeted by the SNP and taken advantage of, insisting they have long been in favour of independence.
The letter states: "As lifelong supporters of independence, it would be strange if we did not support the Yes Scotland campaign. So that is what we have done, nothing more and nothing less. No-one bullied or targeted us, as has been suggested in recent newspaper articles."
The Weirs, who have previously given £1 million to the SNP, also appear to hit back at comments made by Tory MSP and Better Together member Alex Johnstone, who raised concerns over their donations.
When their Yes Scotland contribution was revealed, Mr Johnstone said: "While it's the right of every individual to do whatever they wish with their money, the SNP are clearly taking advantage of these people.
"The thing that has always concerned me about the Weirs is the process behind these donations. Is it entirely their idea? Is it entirely because they are deeply committed to the political principle - or were they approached for donations?
"Were they courted for donations, as many large donors often are? The bottom line is, were they targeted?'
"It simply leaves me a bit uneasy."
In response, the Weirs wrote: "The only 'targeting' has been by an MSP who chose to express his 'concern' for us by implying we have been, at best, naive, and, at worst, duped. Would he, we wonder, have felt the same concern had our contribution supported his cause?"
Mr Johnstone replied: "This letter goes some way to proving my point, and I hope they didn't come under any pressure to write it."
In a rare insight into their lives, the Weirs also explain why they have chosen to stay quiet since their win.The letter states: "On winning the lottery almost three years ago, we made a decision not to speak publicly about any aspect of our lives. We are not celebrities, nor politicians, nor public figures. We try to live quiet, decent lives just as we did before.
"Our silence, though, has meant that, from time to time, we have been subjected to comment and speculation, the majority of it kind and generous, some of it mischievous or ill-informed and, occasionally, some of it has been downright nasty.
"But even we have to say 'enough', when we are denigrated in the most personal of ways."
The couple go on to call for both sides of the independence debate to "stop the smears and personal attacks", adding: "No-one - on any side - should be vilified for the views they hold, lest our democracy become the victim of the present debate.
"Differences can and should be expressed - but decently, with honesty and integrity.
"Our lives have been blessed with good fortune. And we wish to live out our time in a happy and confident Scotland, one which respects and thrives on political differences.
"Otherwise, in a race to the bottom of the political barrel, we will all be the losers."
The Weirs have become known for their generous donations to a number of different causes, including £800,000 to Largs Thistle FC for an artificial pitch and £900,000 towards a sports hall at Inverclyde National Sports Training Centre near Largs.
They also donated their £220,000 former home to a teenage mother who lived next door and provided £115,000-a-year expenses for motor-racing prodigy Gregor Ramsay to fund his place at a prestigious driving academy.