diff --git a/upup/models/cloudup/resources/addons/networking.weave/k8s-1.6.yaml.template b/upup/models/cloudup/resources/addons/networking.weave/k8s-1.6.yaml.template
index 99af954df5854..81954c30203c1 100644
--- a/upup/models/cloudup/resources/addons/networking.weave/k8s-1.6.yaml.template
+++ b/upup/models/cloudup/resources/addons/networking.weave/k8s-1.6.yaml.template
@@ -64,6 +64,8 @@ spec:
       labels:
         name: weave-net
         role.kubernetes.io/networking: "1"
+      annotations:
+        scheduler.alpha.kubernetes.io/critical-pod: ''
     spec:
       containers:
         - name: weave
@@ -136,6 +138,8 @@ spec:
       tolerations:
         - effect: NoSchedule
           operator: Exists
+        - key: CriticalAddonsOnly
+          operator: Exists
       volumes:
         - name: weavedb
           hostPath:
diff --git a/upup/models/cloudup/resources/addons/networking.weave/k8s-1.7.yaml.template b/upup/models/cloudup/resources/addons/networking.weave/k8s-1.7.yaml.template
index 3c74d3b175026..e7ea479a287f2 100644
--- a/upup/models/cloudup/resources/addons/networking.weave/k8s-1.7.yaml.template
+++ b/upup/models/cloudup/resources/addons/networking.weave/k8s-1.7.yaml.template
@@ -64,6 +64,8 @@ spec:
       labels:
         name: weave-net
         role.kubernetes.io/networking: "1"
+      annotations:
+        scheduler.alpha.kubernetes.io/critical-pod: ''
     spec:
       containers:
         - name: weave
@@ -141,6 +143,8 @@ spec:
       tolerations:
         - effect: NoSchedule
           operator: Exists
+        - key: CriticalAddonsOnly
+          operator: Exists
       volumes:
         - name: weavedb
           hostPath:
diff --git a/upup/models/cloudup/resources/addons/networking.weave/pre-k8s-1.6.yaml.template b/upup/models/cloudup/resources/addons/networking.weave/pre-k8s-1.6.yaml.template
index 2880182770500..0b54f06a34d0d 100644
--- a/upup/models/cloudup/resources/addons/networking.weave/pre-k8s-1.6.yaml.template
+++ b/upup/models/cloudup/resources/addons/networking.weave/pre-k8s-1.6.yaml.template
@@ -19,8 +19,9 @@ spec:
   template:
     metadata:
       annotations:
+        scheduler.alpha.kubernetes.io/critical-pod: ''
         scheduler.alpha.kubernetes.io/tolerations: >-
-          [{"key":"dedicated","operator":"Equal","value":"master","effect":"NoSchedule"}]
+          [{"key":"dedicated","operator":"Equal","value":"master","effect":"NoSchedule"},{"key":"CriticalAddonsOnly", "operator":"Exists"}]
       labels:
         name: weave-net
         role.kubernetes.io/networking: "1"