Seems that there isn't any straightforward solution, so we should treat x-axis as continuous in terms of w
and manually compute required positions for ticks and bar centers (this is useful):
# pos is an explicit formula for bar centers that we are interested in:
# last + half(previous_width) + half(current_width)
pos <- 0.5 * (cumsum(w) + cumsum(c(0, w[-length(w)])))
ggplot() +
geom_bar(aes(x = pos, width = w, y = y, fill = x), stat = "identity") +
scale_x_continuous(labels = x, breaks = pos)