Calculating weighted polygon centroids in R

Question

I need to calculate the centroids of a set of spatial zones based on a separate population grid dataset. Grateful for a steer on how to achieve this for the example below.<

Answer 1

The answers by Spacedman and Josh are really great, but I'd like to share two other alternatives which are relatively fast and simple.

library(data.table)
library(spatialEco)
library(raster)
library(rgdal)

using a data.table approach:

# get centroids of raster data
  data_points <- rasterToPoints(dat, spatial=TRUE)

# intersect with polygons
  grid_centroids <- point.in.poly(data_points, polys)

# calculate weighted centroids
  grid_centroids <- as.data.frame(grid_centroids)
  w.centroids <- setDT(grid_centroids)[, lapply(.SD, weighted.mean, w=layer), by=POLYID, .SDcols=c('x','y')]

using wt.centroid{spatialEco} :

  # get a list of the ids from each polygon
    poly_ids <- unique(grid_centroids@data$POLYID)

  # use lapply to calculate the weighted centroids of each individual polygon
    w.centroids.list <- lapply(poly_ids, function(i){wt.centroid( subset(grid_centroids, grid_centroids@data$POLYID ==i)
                                                                  , 'layer', sp = TRUE)} )