The latest gift, on top of £1m donated last year, means the SNP-supporting Ayrshire couple have supplied Yes Scotland with almost 80% of its cash since it was founded in May 2012.
The extent to which Yes Scotland is bankrolled by the Weirs, who scooped £161m in 2011, will be confirmed today when the organisation publishes details of its income since making its last voluntary declaration in April 2013.
The new figures show Yes Scotland has so far received around £4.5m in cash, of which the Weirs have given £3.5m, or 77%.
Overall, Yes Scotland has received £3,151,000 since April 2013, giving a grand total to date, including the SNP help-in-kind, of £4,888,797.
In its first year of operations, Yes Scotland declared £1.6m in income, of which £1m was from the Weirs, and £343,000 was "non-cash" start-up help provided by the SNP. Three other donors gave more than £7500, while some 7000 small donors gave a total of £112,000.
The new donation figures are again dominated by the Weirs, who each gave £1.25m.
Five other large donors - two of whom work at Yes Scotland - gave a further £178,000.
Randall Foggie, an unsuccessful SNP council candidate from Kirkcaldy, gave £60.000.
Yes Scotland operations director Mark Shaw, head of the Hazeldene property group, gave £50,000.
And property developer Dan Macdonald, a member of Yes Scotland's advisory board and an established SNP donor, also gave £50,000.
A Norman Easton gave £10,000 and Highlands author Mary McCabe gave £8000.
Smaller donations - classed as those under £7500 - were more numerous and more generous than in the previous year, with more than 11,000 people giving a total of £473,000.
The pro-Union Better Together campaign has declared donations of just £2.8m up to December 2013.
Without the Weirs giving to the Yes campaign, the No camp would have the financial edge.
Better Together has so far declared two lots of donor figures: in April 2013 it revealed it had received £1.1m since launching in June 2012, and in December it declared a further £1.7m.
Nineteen people donated more than £7500 last year and 17,400 people gave less than £7500, for a total of £341,600.
Better Together's largest donor to date is Donald Houston, owner of the Ardnamurchan Estate and the Adelphi distillery, who has given a total of £600,000 personally and via companies.
Yes Scotland says its donors are all registered to vote in the referendum, whereas many of Better Together's live south of the Border.
The Weirs, who have also endowed a charitable foundation with £5m of their fortune, last week made a rare public statement explaining their support for a Yes vote on September 18, and denied they had been duped or exploited.
"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," they said.
Calling for an end to "smears" and "personal attacks", they revealed: "Our silence ... 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 downright nasty."
Better Together campaign director Blair McDougall said: "No-one would criticise the Weirs, who are longstanding SNP supporters. However, it is extraordinary that compared to the tens of thousands of small donations received by Better Together, almost 80% of Yes Scotland's money comes from one source.
"We now know why they have been hiding their donations for so long."
At present, there are no limits to campaign spending in the referendum.
However, on May 30, the final 16-week "regulated period" begins and sees the start of tight limits for political parties, the official campaign groups and smaller participants.
After May 30, spending by Yes Scotland and Better Together will be capped by law at £1.5m.
The SNP will be allowed to spend £1.344m, Labour £834,000, the Tories £396,000, the Scottish LibDems £201,000 and the Greens £150,000.
A Yes Scotland spokesman said: "We will be making an announcement about donations shortly."