I have not found memory problems with square matrices up to dimension 1000.
@MichaelChirico's suggestion seems to be the most efficient. It runs in time constant with the matrix dimension, unlike diag<-.
The two methods used below are

# create an index
i <- rep(c(FALSE, TRUE), ncol(A) %/% 2)
j <- which(i)

# can also be diag(A)[i]
diag(A)[j] <- W

# cannot be cbind(i, i)
A[cbind(j, j)] <- 0

cbind is clearly more efficient.

library(microbenchmark)
library(ggplot2)

testFun <- function(N) {
  out <- lapply(seq.int(N)[-1L], \(n) {
    A <- matrix(1:n^2, n, n)
    W <- rep(0L, ncol(A) %/% 2L)
    i <- rep(c(FALSE, TRUE), ncol(A) %/% 2)
    j <- which(i)
    mb <- microbenchmark(
      diag = {diag(A)[i] <- W},
      cbind = {A[cbind(j, j)] <- W}
    )
    mb$dim <- n
    mb
  })
  out <- do.call(rbind, out)
  aggregate(time ~ ., out, median)
}

testData <- testFun(1000)
ggplot(testData, aes(dim, time, colour = expr)) +
  geom_line() +
  geom_point() +
  theme_bw()

^{Created on 2024-01-14 with reprex v2.0.2}

Edit

Another way of assigning the diagonal elements of a square matrix is proposed by user20650 in comment. Change the timimg instruction call above to

mb <- microbenchmark(
  diag = {diag(A)[i] <- W},
  cbind = {A[cbind(j, j)] <- W},
  sq = {A[j*j] <- W}
)

and the plot (without diag) becomes