Computing radial-velocities from Cross Correlation data How can I better fit a Gaussian curve to a CCF so that I get the most precise RV value? The image below shows the fitting where I compared the fitting by weighting by the uncertainties and not. There is not a big difference between them because the errors are nearly the same for all data points.

The RV is the $\mu$ and the uncertainty was gotten from the covariance matrix first time in the diagonal. Performing a similar procedure but for summing several orders (such as fig. below) gives me the RV time-series which has too much spread. I need to find a way to reduce the noise as much as possible. I am not showing the errors in RV time-series because I thought it to be coming from the covariance matrix but it looks unrealistic (too big).
Why not fit the orders you are interested in separately and then use the standard error of the mean (possibly weighted by the signal-to-noise in each CCF) as the precision in the final, averaged RV.
In terms of what to fit, I don't see why a Gaussian is so bad? You probably need to limit the fit to the inner $\sim \pm 1 \sigma$ to avoid noise outside the peak pulling the fit one way or another. Other options are to just use the numerical centroid (but this may be affected by asymmetry) or you could use a sinc function to the central region (sometimes a better model of the peak of a CCF).
Edit: You haven't followed my advice, which was to limit the Gaussian fit to $\pm 1$ sigma from the peak (do it iteratively). At the moment, the &quot;wings&quot; of the Gaussian are just adding noise.
As a rule of thumb though, you are not going to do much better than $2.2\sigma$  divided by the signal-to-noise ratio. It looks like your $\sigma \sim 2$ km/s and your signal-to-noise ratio is about 30, so I don't see how you can have gotten a scatter as small as you have from data like this? And the graph below contains no points with the value $-10.76$. There is still something missing from your question.