diff --git a/NEWS.md b/NEWS.md
index 36f3dc49d..743da9c81 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -27,6 +27,7 @@ If you read this from a place other than <https://mc-stan.org/projpred/news/inde
 * Output element `pct_solution_terms_cv` has now also been added to `vsel` objects returned by `varsel()`, but in that case, it is simply `NULL`. This (`pct_solution_terms_cv` being `NULL`) is now also the case if `validate_search = FALSE` was used in `cv_varsel()`.
 * Minor enhancements in the documentation.
 * Enhancements in the vignettes. In particular, section ["Troubleshooting"](https://mc-stan.org/projpred/articles/projpred.html#troubleshooting) of the main vignette has been revised.
+* If `proj_predict()` is used with observation weights that are not all equal to `1`, a warning is now thrown. (GitHub: starts to address #402)
 
 ## Bug fixes
 
diff --git a/R/augdat.R b/R/augdat.R
index 9bc578cf0..9ea46a36e 100644
--- a/R/augdat.R
+++ b/R/augdat.R
@@ -250,18 +250,10 @@ ppd_cats <- function(mu_arr, margin_draws = 3, wobs = 1, return_vec = FALSE) {
     margin_cats <- 2
     bind_fun <- rbind
   }
-  ### Currently unused:
-  # if (length(wobs) == 0) {
-  #   wobs <- rep(1, length(y))
-  # } else if (length(wobs) == 1) {
-  #   wobs <- rep(wobs, length(y))
-  # } else if (length(wobs) != length(y)) {
-  #   stop("Argument `wobs` needs to be of length 0, 1, or `length(y)`.")
-  # }
-  ###
   n_draws <- dim(mu_arr)[margin_draws]
   n_obs <- dim(mu_arr)[margin_obs]
   n_cat <- dim(mu_arr)[margin_cats]
+  wobs <- parse_wobs_ppd(wobs, n_obs = n_obs)
   if (return_vec) {
     stopifnot(n_draws == 1)
     bind_fun <- c
diff --git a/R/extend_family.R b/R/extend_family.R
index 879b0a5cb..4b24f4029 100644
--- a/R/extend_family.R
+++ b/R/extend_family.R
@@ -542,6 +542,7 @@ extend_family_poisson <- function(family) {
     -2 * dpois_log_reduced(x = y, lamb = mu, wobs = weights)
   }
   ppd_poiss <- function(mu, dis, weights = 1) {
+    weights <- parse_wobs_ppd(weights, n_obs = length(mu))
     rpois(length(mu), mu)
   }
 
@@ -592,6 +593,7 @@ extend_family_gaussian <- function(family) {
     -2 * weights * (-0.5 / dis^2 * (y - mu)^2 - log(dis))
   }
   ppd_gauss <- function(mu, dis, weights = 1) {
+    weights <- parse_wobs_ppd(weights, n_obs = length(mu))
     rnorm(length(mu), mu, dis)
   }
 
@@ -639,6 +641,7 @@ extend_family_gamma <- function(family) {
     ## weights*dgamma(y, dis, dis/matrix(mu), log= TRUE)
   }
   ppd_gamma <- function(mu, dis, weights = 1) {
+    weights <- parse_wobs_ppd(weights, n_obs = length(mu))
     rgamma(length(mu), dis, dis / mu)
   }
 
@@ -694,6 +697,7 @@ extend_family_student_t <- function(family) {
                      * log(1 + 1 / family$nu * ((y - mu) / dis)^2) - log(dis)))
   }
   ppd_student_t <- function(mu, dis, weights = 1) {
+    weights <- parse_wobs_ppd(weights, n_obs = length(mu))
     rt(length(mu), family$nu) * dis + mu
   }
 
diff --git a/R/latent.R b/R/latent.R
index 0ed94f643..fa3a83e57 100644
--- a/R/latent.R
+++ b/R/latent.R
@@ -54,6 +54,7 @@ latent_ll_oscale_poiss <- function(ilpreds, y_oscale,
 latent_ppd_oscale_poiss <- function(ilpreds_resamp, wobs, cl_ref,
                                     wdraws_ref = rep(1, length(cl_ref)),
                                     idxs_prjdraws) {
+  wobs <- parse_wobs_ppd(wobs, n_obs = ncol(ilpreds_resamp))
   ppd <- rpois(prod(dim(ilpreds_resamp)), lambda = ilpreds_resamp)
   ppd <- matrix(ppd, nrow = nrow(ilpreds_resamp), ncol = ncol(ilpreds_resamp))
   return(ppd)
diff --git a/R/methods.R b/R/methods.R
index 4e66b2e7c..0ec8afb33 100644
--- a/R/methods.R
+++ b/R/methods.R
@@ -57,7 +57,10 @@
 #' @param ... Arguments passed to [project()] if `object` is not already an
 #'   object returned by [project()].
 #'
-#' @details In case of the latent projection and `transform = FALSE`:
+#' @details Currently, [proj_predict()] ignores observation weights that are not
+#'   equal to `1`. A corresponding warning is thrown if this is the case.
+#'
+#'   In case of the latent projection and `transform = FALSE`:
 #'   * Output element `pred` contains the linear predictors without any
 #'   modifications that may be due to the original response distribution (e.g.,
 #'   for a [brms::cumulative()] model, the ordered thresholds are not taken into
diff --git a/R/misc.R b/R/misc.R
index 90da55e24..17c2f9739 100644
--- a/R/misc.R
+++ b/R/misc.R
@@ -579,3 +579,21 @@ verb_out <- function(..., verbose = TRUE) {
     cat(..., "\n", sep = "")
   }
 }
+
+# Parse the argument containing the observation weights (`wobs` or `weights`)
+# for the <family_object>$ppd() functions used by proj_predict():
+parse_wobs_ppd <- function(wobs, n_obs) {
+  if (length(wobs) == 0) {
+    wobs <- rep(1, n_obs)
+  } else if (length(wobs) == 1) {
+    wobs <- rep(wobs, n_obs)
+  } else if (length(wobs) != n_obs) {
+    stop("Argument `wobs` needs to be of length 0, 1, or the number of ",
+         "observations.")
+  }
+  if (!all(wobs == 1) && getOption("projpred.warn_wobs_ppd", TRUE)) {
+    warning("Currently, proj_predict() ignores observation weights not equal ",
+            "to `1`.")
+  }
+  return(wobs)
+}
diff --git a/man/pred-projection.Rd b/man/pred-projection.Rd
index 918045df4..aa3b69d18 100644
--- a/man/pred-projection.Rd
+++ b/man/pred-projection.Rd
@@ -152,6 +152,9 @@ submodels at once (for \code{object}s of class \code{vsel} or \code{object}s ret
 \code{\link[=project]{project()}} call to an object of class \code{vsel}; see \code{\link[=project]{project()}}).
 }
 \details{
+Currently, \code{\link[=proj_predict]{proj_predict()}} ignores observation weights that are not
+equal to \code{1}. A corresponding warning is thrown if this is the case.
+
 In case of the latent projection and \code{transform = FALSE}:
 \itemize{
 \item Output element \code{pred} contains the linear predictors without any
diff --git a/tests/testthat/setup.R b/tests/testthat/setup.R
index f35d17ef6..001697675 100644
--- a/tests/testthat/setup.R
+++ b/tests/testthat/setup.R
@@ -812,6 +812,9 @@ meth_tst <- list(
 # Suppress the warning for interaction terms being selected before all involved
 # main effects have been selected (only concerns L1 search):
 options(projpred.warn_L1_interactions = FALSE)
+# Suppress the warning thrown by proj_predict() in case of observation weights
+# that are not all equal to `1`:
+options(projpred.warn_wobs_ppd = FALSE)
 
 search_trms_tst <- list(
   default_search_trms = list(),