Speaking to TalkRADIO, Mr Weir claimed the EU Brexit offer envisages Northern Ireland remaining in the single market forced to abide EU laws post-Brexit.
The DUP MLA argued the “key single market” Northern Ireland shares with the rest of the UK would be compromised by the EU proposal.
He said: “The complication that has been raised sometimes with Canada plus plus plus – because it’s sometimes been indicated that is something the EU has on offer.
“But what they’ve put on offer so far is purely Canada plus plus plus for Great Britain rather than the whole of the United Kingdom.
“The position of the EU would envisage Northern Ireland certainly remaining within the single market, accepting all the regulations of the EU.
“And I think both on a democratic and a constitutional point – let alone the economics of this- we would be in a position where we would simply have to accept all the rules of the EU without having any degree of input on what was happening and that is something which is completely unacceptable.
“But our focus, particularly in terms of borders, is that roughly 70 percent of our trade in Northern Ireland goes to Great Britain.
“That’s the key single market for us.”
It comes as Mr Weir’s party has threatened to vote down the upcoming Budget if Mrs May pushes on with plans to accept a number of regulatory checks between Northern Ireland and Great Britain.
DUP MPs, on Wednesday evening, abstained in a minor agricultural vote in Westminster to show they are not afraid to strong-arm the Government over proposed plans for the Irish backstop.
The Prime Minister relies on the support of 10 of Northern Ireland’s DUP MPs to prop her up in the House of Commons.
DUP leader Arlene Foster agreed on a so-called Confidence and Supply deal with Mrs May after the election, in which the DUP offered its support on budget and Brexit matters.
Last night, DUP MPs moved to show the Government that their threat was by abstaining in a vote on the Agriculture Bill.
Party sources said the decision by MPs to sit out of the vote is designed to be seen as a warning shot to Mrs May.
Mr Weir said: “We have made it abundantly clear that we have one red line in this process as we don’t want to see effectively an economic border which would be damaging to both the union and damaging to Northern Ireland business if put in place down in the Irish Sea.
“That is something that is fundamentally important to us and it’s important to people when they’re making decisions do so in the knowledge of the implications.
“We hope that that would be something that will be avoided.
“The decision that will be taken, potentially in the next week or two, will have implications perhaps for decades to come, not just for Northern Ireland but for the whole of UK.”
Source : EXPRESS