Weighted means are pretty common in my experience.
The current workaround is pretty awkward (I might be using a weird approach, CMIIW):
x = 1:10
w = 10:1
frollapply(seq_along(x), n = 3, function(i) stats::weighted.mean(x[i], w[i]))
# [1] NA NA 1.925926 2.916667 3.904762 4.888889 5.866667 6.833333 7.777778 8.666667