I'm currently working on a physics project where I am basically using logger pro's video analysis to find speeds for an object being accelerated by an object. Furthermore, I am conducting multiple trials in order to get averaged values. I have propagated the uncertainty assuming that the major source of uncertainty is where I mark the object in logger pro and I have assumed that this uncertainty will be the same for all trials. However, although I am assuming each marker has the same uncertainty my final values that I get at the end of each trial end up having different uncertainties. This is why I decided to use a weighted mean (to account for uncertainty). But if I am assuming all initial "measurements" have the same uncertainty and I am using the same data analysis methods and calculations for each trial should I really weight them differently?
TLDR; I want to average a value produced from multiple trials and I am assuming the source of uncertainty is the same for all trials but the final uncertainties end up being different. Should I use a weighted mean or a regular mean?