Effective Nyquist frequency / signal resolution for overlapping time averaged signal samples
The process that you are describing can be broken down into two steps


Filter with a moving average filter with length $t_{width}$
Sampling with an interval $delta\_t$


A moving average filter is a low pass filter, but not a very good with lots of side lobes. It will help reduce aliasing in the sample process, but it won't eliminate it with any type of hard "threshold". The longer $t_{width}$ is and the the smaller $delta\_t$ is the less aliasing you get.

I think you approaching this backwards: Your "time resolution" is simply determined by the highest frequency in the signal. You need to determine this first and work backwards from there.

In practice, there is always aliasing. No real world signal is actually bandwidth limited in the mathematical sense. So you need to determine the frequency range "of interest", figure out how much energy the signal has outside this region, determine how much noise or aliasing you can tolerate, and design a suitable anti-aliasing filter to meet your specific requirements.