You can't directly supply weights as an option to laqcurvefit.
Better is to use lsqnonlin for this, since you return the residuals.
Create a vector for the weights I've called it w here. Small, where you want the weight for a point to be small.
AntoineW = @(Param,x,y,w) w.*(y - (Param(1)+(Param(2)./(x+Param(3)))+Param(4).*x + Param(5).*log(x)+Param(6).*(x.^Param(7))));
Param0 = [... stuff ...]
ParamEst = lsqnonlin(@(Param) Antoine(Param,x,y,w), Param0, lb, ub, options); %antoine parameters
As you should see, this scales the residuals in that area by an amount you can define in the vector w.
Set your options up for lsqnonlin. By the way, setting the tolerances that tiny can be of little real value. These algorithms tend to be quadratically convergent near the solution. But setting really tiny tolerances may just make the code work very hard at the end, wasting a lot of time for no gain as it tries to refine the least significant bits of the result.
