diff --git a/core/modules/media_library/src/Plugin/Field/FieldWidget/MediaLibraryWidget.php b/core/modules/media_library/src/Plugin/Field/FieldWidget/MediaLibraryWidget.php
index ac9cb3b510..bbc6d4f9cc 100644
--- a/core/modules/media_library/src/Plugin/Field/FieldWidget/MediaLibraryWidget.php
+++ b/core/modules/media_library/src/Plugin/Field/FieldWidget/MediaLibraryWidget.php
@@ -350,10 +350,12 @@ public function formElement(FieldItemListInterface $items, $delta, array $elemen
       // @todo Use a <button> link here, and delete
       // seven_preprocess_fieldset__media_library_widget(), when
       // https://www.drupal.org/project/drupal/issues/2999549 lands.
+      $count_referenced_entities = count($referenced_entities);
       $element['#field_prefix']['weight_toggle'] = [
         '#type' => 'html_tag',
         '#tag' => 'button',
         '#value' => $this->t('Show media item weights'),
+        '#access' => $count_referenced_entities > 1,
         '#attributes' => [
           'class' => [
             'link',
@@ -424,6 +426,7 @@ public function formElement(FieldItemListInterface $items, $delta, array $elemen
           '#type' => 'number',
           '#theme' => 'input__number__media_library_item_weight',
           '#title' => $this->t('Weight'),
+          '#access' => $count_referenced_entities > 1,
           '#default_value' => $delta,
           '#attributes' => [
             'class' => [
diff --git a/core/modules/media_library/tests/src/FunctionalJavascript/EntityReferenceWidgetTest.php b/core/modules/media_library/tests/src/FunctionalJavascript/EntityReferenceWidgetTest.php
index 4d8ee6060f..5cd5d0fff9 100644
--- a/core/modules/media_library/tests/src/FunctionalJavascript/EntityReferenceWidgetTest.php
+++ b/core/modules/media_library/tests/src/FunctionalJavascript/EntityReferenceWidgetTest.php
@@ -191,11 +191,10 @@ public function testWidget() {
     // Assert the focus is set back on the open button of the media field.
     $this->assertJsCondition('jQuery("#field_twin_media-media-library-wrapper .js-media-library-open-button").is(":focus")');
 
-    // Assert that we can toggle the visibility of the weight inputs.
+    // The toggle for weight input's visibility should not be available when
+    // the field contains a single item.
     $wrapper = $assert_session->elementExists('css', '.field--name-field-twin-media');
-    $wrapper->pressButton('Show media item weights');
-    $assert_session->fieldExists('Weight', $wrapper)->click();
-    $wrapper->pressButton('Hide media item weights');
+    $assert_session->fieldNotExists('Weight', $wrapper);
 
     // Remove the selected item.
     $button = $assert_session->buttonExists('Remove', $wrapper);
@@ -213,6 +212,15 @@ public function testWidget() {
     $page->checkField('Select Dog');
     $this->pressInsertSelected('Added one media item.');
 
+    // Assert that we can toggle the visibility of the weight inputs when the
+    // field contains more than one item.
+    $wrapper = $assert_session->elementExists('css', '.field--name-field-twin-media');
+    $wrapper->pressButton('Show media item weights');
+    // It's to ensure that the styling doesn't accidentally render it
+    // unclickable.
+    $assert_session->fieldExists('Weight', $wrapper)->click();
+    $wrapper->pressButton('Hide media item weights');
+
     // Assert the same has been added twice and remove the items again.
     $this->waitForElementsCount('css', '.field--name-field-twin-media [data-media-library-item-delta]', 2);
     $assert_session->hiddenFieldValueEquals('field_twin_media[selection][0][target_id]', 4);
diff --git a/core/modules/media_library/tests/src/FunctionalJavascript/WidgetAnonymousTest.php b/core/modules/media_library/tests/src/FunctionalJavascript/WidgetAnonymousTest.php
index 089c870668..6d1d68d1b7 100644
--- a/core/modules/media_library/tests/src/FunctionalJavascript/WidgetAnonymousTest.php
+++ b/core/modules/media_library/tests/src/FunctionalJavascript/WidgetAnonymousTest.php
@@ -21,6 +21,7 @@ protected function setUp() {
     // Create a few example media items for use in selection.
     $this->createMediaItems([
       'type_one' => [
+        'Cat',
         'Dog',
       ],
     ]);
@@ -60,12 +61,24 @@ public function testWidgetAnonymous() {
 
     // Ensure that the selection completed successfully.
     $this->waitForText('Dog');
+    $assert_session->fieldNotExists('Weight');
+
+    // Add to the unlimited cardinality field.
+    $this->openMediaLibraryForField('field_unlimited_media');
+
+    // Select the second media item (should be Cat).
+    $this->selectMediaItem(1);
+    $this->pressInsertSelected('Added one media item.');
+
+    // Ensure that the selection completed successfully.
+    $this->waitForText('Cat');
 
     // Save the form.
     $assert_session->elementExists('css', '.js-media-library-widget-toggle-weight')->click();
     $this->submitForm([
       'title[0][value]' => 'My page',
       'field_unlimited_media[selection][0][weight]' => '0',
+      'field_unlimited_media[selection][1][weight]' => '1',
     ], 'Save');
     $assert_session->pageTextContains('Basic Page My page has been created');
     $assert_session->pageTextContains('Dog');