diff --git a/tests/test_device.py b/tests/test_device.py
index 843db9a83..0275082a1 100644
--- a/tests/test_device.py
+++ b/tests/test_device.py
@@ -49,7 +49,7 @@
 from zha.application.platforms import PlatformEntity
 from zha.application.platforms.binary_sensor import IASZone
 from zha.application.platforms.light import Light
-from zha.application.platforms.sensor import LQISensor, RSSISensor
+from zha.application.platforms.sensor import Battery, LQISensor, RSSISensor
 from zha.application.platforms.sensor.device_class import (
     SensorDeviceClass,
     SensorStateClass,
@@ -948,6 +948,31 @@ async def test_primary_entity_computation(
         ]
 
 
+async def test_primary_entity_weight_0_not_elected(zha_gateway: Gateway) -> None:
+    """Test a weight-0 entity is not elected primary, even as the sole candidate."""
+
+    # Without the `Basic` cluster, no LQI/RSSI entities are created, so the
+    # battery entity is the only entity of this device
+    zigpy_dev = create_mock_zigpy_device(
+        zha_gateway,
+        {
+            1: {
+                SIG_EP_INPUT: [general.PowerConfiguration.cluster_id],
+                SIG_EP_OUTPUT: [],
+                SIG_EP_TYPE: zigpy.profiles.zha.DeviceType.SIMPLE_SENSOR,
+                SIG_EP_PROFILE: zigpy.profiles.zha.PROFILE_ID,
+            }
+        },
+    )
+    zha_device = await join_zigpy_device(zha_gateway, zigpy_dev)
+
+    battery = get_entity(zha_device, Platform.SENSOR, entity_type=Battery)
+    assert list(zha_device.platform_entities.values()) == [battery]
+
+    # The weight-0 battery entity is not elected as the primary entity
+    assert not battery.primary
+
+
 async def test_quirks_v2_primary_entity(zha_gateway: Gateway) -> None:
     """Test quirks v2 primary entity."""
     registry = DeviceRegistry()
diff --git a/zha/zigbee/device.py b/zha/zigbee/device.py
index 51f8895b3..90dfd4547 100644
--- a/zha/zigbee/device.py
+++ b/zha/zigbee/device.py
@@ -1625,9 +1625,13 @@ def _compute_primary_entity(self, entities: Sequence[PlatformEntity]) -> None:
         # It should not be possible for there to be more than one
         assert not explicitly_primary
 
-        # For weight matching, only consider non-counter entities and entities which are
-        # not explicitly marked as not primary
-        candidates = [e for e in entities if e.enabled and e._attr_primary is not False]
+        # For weight matching, only consider entities with a non-zero primary weight
+        # which are not explicitly marked as not primary
+        candidates = [
+            e
+            for e in entities
+            if e.enabled and e._attr_primary is not False and e.primary_weight > 0
+        ]
         candidates.sort(reverse=True, key=lambda e: e.primary_weight)
 
         if not candidates: