The Prime Minister said a new independence vote would cause continued 'political stagnation'.
The European Union (Withdrawal Agreement) Bill was passed by 330 votes to 231.
Proceedings were disrupted twice by hecklers in the gallery, who were led away by police.
Boris Johnson told MPs during Prime Minister's Questions that the people of Scotland "voted decisively" in 2014 to stay in the UK in a "once in a generation choice".
Ex-justice secretary Kenny MacAskill - and newly-elected MP - said a longer wait is 'no bad thing'.
Scottish party leaders delivered their New Year messages ahead of the start of a new decade.
Mr Weir, who won £161m in the EuroMillions in 2011, died on Friday after a short illness.
Former RBS chief executive Ross McEwan, actress Maureen Beattie and ex-politician Brian Wilson are also recognised.
Scotland's First Minister has thanked festive volunteers and public-sector workers in her festive message.
Holyrood backed the Referendums (Scotland) Bill at its final stage by 68 votes to 54.
As Boris Johnson's government lays out its legislative agenda, it dismisses a 2020 indyref as a 'damaging distraction'.
The First Minister has called for the Prime Minister to 'agree and negotiate' the transfer of powers to Holyrood to hold indyref2.
The First Minister said there is 'growing cross-party recognition' the question of a second vote should not be decided at Westminster.
The First Minister will invite people in Scotland to come together to back another referendum.
The UK Government has ruled out a second Scottish independence referendum.
She warned Boris Johnson: 'Scotland cannot be imprisoned in the Union against its will.'
Nicola Sturgeon has told the PM he can't 'bludgeon' Scotland into seeing the world the way he does.
Nicola Sturgeon responds cautiously to prediction her party will win 55 of 59 Scottish seats.
The SNP are on course to win 55 seats, up 20 and their second best result of all time.
She was challenged by Jackson Carlaw at the final FMQs before the general election.