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 d23f11538ff6ca0a31146cf950953f4770278752..bc9c9b01cef9e070acc855322b7f8140cabb573a 100644
--- a/core/modules/media_library/src/Plugin/Field/FieldWidget/MediaLibraryWidget.php
+++ b/core/modules/media_library/src/Plugin/Field/FieldWidget/MediaLibraryWidget.php
@@ -333,6 +333,7 @@ public function formElement(FieldItemListInterface $items, $delta, array $elemen
       return $element;
     }
 
+    $multiple_items = FALSE;
     if (empty($referenced_entities)) {
       $element['#field_prefix']['empty_selection'] = [
         '#markup' => $this->t('No media items are selected.'),
@@ -342,10 +343,12 @@ 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.
+      $multiple_items = count($referenced_entities) > 1;
       $element['#field_prefix']['weight_toggle'] = [
         '#type' => 'html_tag',
         '#tag' => 'button',
         '#value' => $this->t('Show media item weights'),
+        '#access' => $multiple_items,
         '#attributes' => [
           'class' => [
             'link',
@@ -416,6 +419,7 @@ public function formElement(FieldItemListInterface $items, $delta, array $elemen
           '#type' => 'number',
           '#theme' => 'input__number__media_library_item_weight',
           '#title' => $this->t('Weight'),
+          '#access' => $multiple_items,
           '#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 549a3c70502aaa35f3953ecf917ad22290ccbe9e..01e70e28235923f8501810306d68a63df533c59b 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 inputs' 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->elementNotExists('named', ['button', 'Show media item weights'], $wrapper);
 
     // Remove the selected item.
     $button = $assert_session->buttonExists('Remove', $wrapper);
@@ -212,6 +211,14 @@ public function testWidget() {
     $this->openMediaLibraryForField('field_twin_media');
     $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');
+    // Ensure that the styling doesn't accidentally render the weight field
+    // unusable.
+    $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);
diff --git a/core/modules/media_library/tests/src/FunctionalJavascript/WidgetAnonymousTest.php b/core/modules/media_library/tests/src/FunctionalJavascript/WidgetAnonymousTest.php
index 1bccf2034a9f729576a8b2151b022c37a400aaaa..1a6ab1925b679c38d65c2f05f542953182cdfce2 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(): void {
     // Create a few example media items for use in selection.
     $this->createMediaItems([
       'type_one' => [
+        'Cat',
         'Dog',
       ],
     ]);
@@ -60,12 +61,23 @@ 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');
diff --git a/core/themes/claro/css/theme/media-library.css b/core/themes/claro/css/theme/media-library.css
index b41f78eac044bc8a43868cec4f5d250ffac541d4..92916066102dac205c8aaaf591498a6302acfe5c 100644
--- a/core/themes/claro/css/theme/media-library.css
+++ b/core/themes/claro/css/theme/media-library.css
@@ -478,9 +478,16 @@
 
 .media-library-item__preview {
   padding-bottom: 34px;
+}
+
+.field--widget-media-library-widget .media-library-item__preview {
   cursor: move;
 }
 
+.field--widget-media-library-widget .js-media-library-item:only-child .media-library-item__preview {
+  cursor: inherit;
+}
+
 .media-library-item__status {
   position: absolute;
   top: 40px;
diff --git a/core/themes/claro/css/theme/media-library.pcss.css b/core/themes/claro/css/theme/media-library.pcss.css
index 78970b4dcda9c3cc1a6e81f79d5792efa9195dca..3ae30c17994928c9f2fc63a0e733604e8a1336dc 100644
--- a/core/themes/claro/css/theme/media-library.pcss.css
+++ b/core/themes/claro/css/theme/media-library.pcss.css
@@ -440,9 +440,16 @@
 /* Media library entity view display styles. */
 .media-library-item__preview {
   padding-bottom: 34px;
+}
+
+.field--widget-media-library-widget .media-library-item__preview {
   cursor: move;
 }
 
+.field--widget-media-library-widget .js-media-library-item:only-child .media-library-item__preview {
+  cursor: inherit;
+}
+
 .media-library-item__status {
   position: absolute;
   top: 40px;
diff --git a/core/themes/seven/css/theme/media-library.css b/core/themes/seven/css/theme/media-library.css
index 80217a64bcf29a221a494c8aa87c14a7415e00e5..bef8cc6136232034aee4394070e48dffcdafd1c4 100644
--- a/core/themes/seven/css/theme/media-library.css
+++ b/core/themes/seven/css/theme/media-library.css
@@ -456,9 +456,16 @@
 /* Media library entity view display styles. */
 .media-library-item__preview {
   padding-bottom: 34px;
+}
+
+.field--widget-media-library-widget .media-library-item__preview {
   cursor: move;
 }
 
+.field--widget-media-library-widget .js-media-library-item:only-child .media-library-item__preview {
+  cursor: inherit;
+}
+
 .media-library-item__status {
   position: absolute;
   top: 40px;