"a fully managed TimescaleDB service"
Weighted averaging as a commercial service, all by itself? The SQL solution seems complicated, but this is a task easily performed on time-ordered data.
I had to code such a time-weighted average last year, for a game client. The client gets updates for moving objects when they move a small distance or when some dwell time has elapsed. I needed a smoothed velocity from those irregularly spaced samples. The math had to be worked out, but it was just two lines of C++ in the implementation.[1]
filtermult = 1.0f - 1.0f / pow(1.0f + 1.0f / fsRegionCrossingSmoothingTime, secs); // filter scale factor
mFiltered = val * filtermult + mFiltered * (1.0f - filtermult); // low pass filter