diff --git a/mne/time_frequency/tfr.py b/mne/time_frequency/tfr.py
index 1829bb1bb98..52ebcd2c1f3 100644
--- a/mne/time_frequency/tfr.py
+++ b/mne/time_frequency/tfr.py
@@ -2785,6 +2785,7 @@ class AverageTFR(BaseTFR):
     %(nave_tfr_attr)s
     %(sfreq_tfr_attr)s
     %(shape_tfr_attr)s
+    %(weights_tfr_attr)s
 
     See Also
     --------
@@ -2901,10 +2902,15 @@ def __getstate__(self):
 
     def __setstate__(self, state):
         """Unpack AverageTFR from serialized format."""
-        if state["data"].ndim != 3:
-            raise ValueError(f"RawTFR data should be 3D, got {state['data'].ndim}.")
+        if state["data"].ndim not in [3, 4]:
+            raise ValueError(
+                f"RawTFR data should be 3D or 4D, got {state['data'].ndim}."
+            )
         # Set dims now since optional tapers makes it difficult to disentangle later
-        state["dims"] = ("channel", "freq", "time")
+        state["dims"] = ("channel",)
+        if state["data"].ndim == 4:
+            state["dims"] += ("taper",)
+        state["dims"] += ("freq", "time")
         super().__setstate__(state)
         self._comment = state.get("comment", "")
         self._nave = state.get("nave", 1)
@@ -2948,6 +2954,7 @@ class AverageTFRArray(AverageTFR):
         The number of averaged TFRs.
     %(comment_averagetfr_attr)s
     %(method_tfr_array)s
+    %(weights_tfr_array)s
 
     Attributes
     ----------
@@ -2960,6 +2967,7 @@ class AverageTFRArray(AverageTFR):
     %(nave_tfr_attr)s
     %(sfreq_tfr_attr)s
     %(shape_tfr_attr)s
+    %(weights_tfr_attr)s
 
     See Also
     --------
@@ -2970,12 +2978,22 @@ class AverageTFRArray(AverageTFR):
     """
 
     def __init__(
-        self, info, data, times, freqs, *, nave=None, comment=None, method=None
+        self,
+        info,
+        data,
+        times,
+        freqs,
+        *,
+        nave=None,
+        comment=None,
+        method=None,
+        weights=None,
     ):
         state = dict(info=info, data=data, times=times, freqs=freqs)
-        for name, optional in dict(nave=nave, comment=comment, method=method).items():
-            if optional is not None:
-                state[name] = optional
+        optional = dict(nave=nave, comment=comment, method=method, weights=weights)
+        for name, value in optional.items():
+            if value is not None:
+                state[name] = value
         self.__setstate__(state)