How to fit a Gaussian considering parameter bound limits and weight?

I have and x and I want to fit it with a Gaussian. I have been using weighted 'fitnlm' for this purpose, but now I also want to fix the upper and lower limit of the fit parameters. I have read that the boundation is possible only with LSQCURVEFIT but at the same time this is not capable of weigh the y values.

Is there any method so that I can weigh the y values as well as bound the resulting parameters together?

(is there any such update on fitnlm?)

Thanks you.