diff --git a/e2e/cgroups/cgroups.go b/e2e/cgroups/cgroups.go
index 9d888295de..3fe24ada26 100644
--- a/e2e/cgroups/cgroups.go
+++ b/e2e/cgroups/cgroups.go
@@ -615,11 +615,12 @@ var resourceFlagTests = []resourceFlagTest{
 		controllerV1:    "cpu",
 		resourceV1:      "cpu.shares",
 		expectV1:        "123",
-		// Cgroups v2 has a conversion from shares to weight:
-		// weight = (1 + ((cpuShares-2)*9999)/262142)
+		// Cgroups v2 has a conversion from shares to weight. The formula has
+		// changed between opencontainer/cgroups versions, and runc / crun
+		// versions. See https://github.com/opencontainers/cgroups/pull/20
 		delegationV2: "cpu",
 		resourceV2:   "cpu.weight",
-		expectV2:     "5",
+		expectV2:     "5|20",
 	},
 	{
 		name:            "cpuset-cpus",
@@ -729,7 +730,7 @@ func (c *ctx) actionFlagV1(t *testing.T, tt resourceFlagTest, profile e2e.Profil
 
 	exitFunc := []e2e.SingularityCmdResultOp{}
 	if tt.expectV1 != "" {
-		exitFunc = []e2e.SingularityCmdResultOp{e2e.ExpectOutput(e2e.ContainMatch, tt.expectV1)}
+		exitFunc = []e2e.SingularityCmdResultOp{e2e.ExpectOutput(e2e.RegexMatch, tt.expectV1)}
 	}
 
 	args := tt.args
@@ -759,7 +760,7 @@ func (c *ctx) actionFlagV2(t *testing.T, tt resourceFlagTest, profile e2e.Profil
 
 	exitFunc := []e2e.SingularityCmdResultOp{}
 	if tt.expectV2 != "" {
-		exitFunc = []e2e.SingularityCmdResultOp{e2e.ExpectOutput(e2e.ContainMatch, tt.expectV2)}
+		exitFunc = []e2e.SingularityCmdResultOp{e2e.ExpectOutput(e2e.RegexMatch, tt.expectV2)}
 	}
 
 	// Use shell in the container to find container cgroup and cat the value for the tested controller & resource.
diff --git a/go.mod b/go.mod
index 333b111017..5747d58786 100644
--- a/go.mod
+++ b/go.mod
@@ -37,7 +37,7 @@ require (
 	github.com/moby/sys/user v0.4.0
 	github.com/moby/sys/userns v0.1.0
 	github.com/moby/term v0.5.2
-	github.com/opencontainers/cgroups v0.0.2
+	github.com/opencontainers/cgroups v0.0.3
 	github.com/opencontainers/image-spec v1.1.1
 	github.com/opencontainers/runc v1.3.0
 	github.com/opencontainers/runtime-spec v1.2.1
diff --git a/go.sum b/go.sum
index 6ad60ba22f..108182631a 100644
--- a/go.sum
+++ b/go.sum
@@ -672,8 +672,8 @@ github.com/onsi/gomega v1.37.0 h1:CdEG8g0S133B4OswTDC/5XPSzE1OeP29QOioj2PID2Y=
 github.com/onsi/gomega v1.37.0/go.mod h1:8D9+Txp43QWKhM24yyOBEdpkzN8FvJyAwecBgsU4KU0=
 github.com/open-policy-agent/opa v1.1.0 h1:HMz2evdEMTyNqtdLjmu3Vyx06BmhNYAx67Yz3Ll9q2s=
 github.com/open-policy-agent/opa v1.1.0/go.mod h1:T1pASQ1/vwfTa+e2fYcfpLCvWgYtqtiUv+IuA/dLPQs=
-github.com/opencontainers/cgroups v0.0.2 h1:A+mAPPMfgKNCEZUUtibESFx06uvhAmvo8sSz3Abwk7o=
-github.com/opencontainers/cgroups v0.0.2/go.mod h1:s8lktyhlGUqM7OSRL5P7eAW6Wb+kWPNvt4qvVfzA5vs=
+github.com/opencontainers/cgroups v0.0.3 h1:Jc9dWh/0YLGjdy6J/9Ln8NM5BfTA4W2BY0GMozy3aDU=
+github.com/opencontainers/cgroups v0.0.3/go.mod h1:s8lktyhlGUqM7OSRL5P7eAW6Wb+kWPNvt4qvVfzA5vs=
 github.com/opencontainers/go-digest v1.0.0 h1:apOUWs51W5PlhuyGyz9FCeeBIOUDA/6nW8Oi/yOhh5U=
 github.com/opencontainers/go-digest v1.0.0/go.mod h1:0JzlMkj0TRzQZfJkVvzbP0HBR3IKzErnv2BNG4W4MAM=
 github.com/opencontainers/image-spec v1.1.1 h1:y0fUlFfIZhPF1W537XOLg0/fcx6zcHCJwooC2xJA040=