Hi /sci/, could some of you big-brained stats bros help out a retarded compchem PhD student?

Pic related is a dataset produced by a molecular dynamics simulation. You don't need to care what it is exactly but I can explain if anyone is interested. I want to understand how to obtain the true uncertainty in my mean observations. The error bars I have for each mean are the two-sided 95% confidence intervals obtained from the standard errors, which were in turn obtained by block averaging the individual observations. The values further along the x-axis have much larger errors as there are fewer observations available to compute those averages.

However, the model I have means I expect this data to exponentially decay (straight line in log-linear plot) and indeed the later points, though they have huge errors, still obey this very well. Intuitively, their mutual close agreement with the trend line implies that the uncertainty is lower than my block averaging tells me. Is there a rigorous way of accounting for this internal correlation when deciding uncertainty, given my model?

I hope I was able make sense.