Convolution with Gaussian filter with fixed resolution for non-uniform data?

I have non unifrom data (x,y) (attached, simplified). I need to use gaussin filter of fixed window size with fixed resolution. Finally I have to use convolution of gaussian filtered data with y.

I know how to do for whole data without bothering about resolution,as follows. It works fine.

sigma = std(x);
gaussFilter =gausswin(3*sigma+1)';
a=gaussFilter/sum(gaussFilter);
abx=conv(y,a,'same');

But resolution is very important for my case. When I consider the resolution, I am blanck. I tried like one below (with resolution 0.5) but failed.

sigma = std(x); %fixed window size
xn=zeros(1,ceil(max(x)));
 for k=1:0.5:size(xn,2) %gives resolution 
    gaussFilter(k)=gausswin(3*sigma+1)';
    xa(k)=gaussFilter(k)/sum(gaussFilter(k));%normalization
 end
 abx=conv(y,xa,'same');
 
 It means I use Gaussian filter of fixed window size at all x=1:0.5:end. Another question is that, Can Gausswin be used for non-uniform data?
 Thank you so much.