diff --git a/x/group/keeper/invariants.go b/x/group/keeper/invariants.go
index 2212573485..1d222e91d8 100644
--- a/x/group/keeper/invariants.go
+++ b/x/group/keeper/invariants.go
@@ -167,6 +167,7 @@ func GroupTotalWeightInvariantHelper(ctx sdk.Context, key storetypes.StoreKey, g
 			msg += fmt.Sprintf("error while returning group member iterator for group with ID %d\n%v\n", groupInfo.Id, err)
 			return msg, broken
 		}
+		defer memIt.Close()
 
 		for {
 			_, err = memIt.LoadNext(&groupMember)
@@ -184,7 +185,6 @@ func GroupTotalWeightInvariantHelper(ctx sdk.Context, key storetypes.StoreKey, g
 				return msg, broken
 			}
 		}
-		memIt.Close()
 
 		groupWeight, err := groupmath.NewNonNegativeDecFromString(groupInfo.GetTotalWeight())
 		if err != nil {
diff --git a/x/group/simulation/operations.go b/x/group/simulation/operations.go
index 43d5da6ed3..22ac6138c9 100644
--- a/x/group/simulation/operations.go
+++ b/x/group/simulation/operations.go
@@ -67,7 +67,7 @@ const (
 	WeightMsgSubmitProposal                  = 90
 	WeightMsgVote                            = 90
 	WeightMsgExec                            = 90
-	WeightMsgLeaveGroup                      = 20
+	WeightMsgLeaveGroup                      = 5
 	WeightMsgUpdateGroupMetadata             = 5
 	WeightMsgUpdateGroupAdmin                = 5
 	WeightMsgUpdateGroupMembers              = 5
@@ -188,10 +188,6 @@ func WeightedOperations(
 			weightMsgCreateGroupPolicy,
 			SimulateMsgCreateGroupPolicy(ak, bk, k),
 		),
-		simulation.NewWeightedOperation(
-			weightMsgLeaveGroup,
-			SimulateMsgLeaveGroup(k, ak, bk),
-		),
 		simulation.NewWeightedOperation(
 			weightMsgCreateGroupWithPolicy,
 			SimulateMsgCreateGroupWithPolicy(ak, bk),
@@ -235,6 +231,10 @@ func WeightedOperations(
 			weightMsgUpdateGroupPolicyMetadata,
 			SimulateMsgUpdateGroupPolicyMetadata(ak, bk, k),
 		),
+		simulation.NewWeightedOperation(
+			weightMsgLeaveGroup,
+			SimulateMsgLeaveGroup(k, ak, bk),
+		),
 	}
 
 	return append(wPreCreateProposalOps, append(createProposalOps, wPostCreateProposalOps...)...)
diff --git a/x/group/simulation/operations_test.go b/x/group/simulation/operations_test.go
index b1981d7932..12f476b88a 100644
--- a/x/group/simulation/operations_test.go
+++ b/x/group/simulation/operations_test.go
@@ -53,7 +53,6 @@ func (suite *SimTestSuite) TestWeightedOperations() {
 	}{
 		{simulation.WeightMsgCreateGroup, group.MsgCreateGroup{}.Route(), simulation.TypeMsgCreateGroup},
 		{simulation.WeightMsgCreateGroupPolicy, group.MsgCreateGroupPolicy{}.Route(), simulation.TypeMsgCreateGroupPolicy},
-		{simulation.WeightMsgLeaveGroup, group.MsgLeaveGroup{}.Route(), simulation.TypeMsgLeaveGroup},
 		{simulation.WeightMsgCreateGroupWithPolicy, group.MsgCreateGroupWithPolicy{}.Route(), simulation.TypeMsgCreateGroupWithPolicy},
 		{simulation.WeightMsgSubmitProposal, group.MsgSubmitProposal{}.Route(), simulation.TypeMsgSubmitProposal},
 		{simulation.WeightMsgSubmitProposal, group.MsgSubmitProposal{}.Route(), simulation.TypeMsgSubmitProposal},
@@ -66,6 +65,7 @@ func (suite *SimTestSuite) TestWeightedOperations() {
 		{simulation.WeightMsgUpdateGroupPolicyAdmin, group.MsgUpdateGroupPolicyAdmin{}.Route(), simulation.TypeMsgUpdateGroupPolicyAdmin},
 		{simulation.WeightMsgUpdateGroupPolicyDecisionPolicy, group.MsgUpdateGroupPolicyDecisionPolicy{}.Route(), simulation.TypeMsgUpdateGroupPolicyDecisionPolicy},
 		{simulation.WeightMsgUpdateGroupPolicyMetadata, group.MsgUpdateGroupPolicyMetadata{}.Route(), simulation.TypeMsgUpdateGroupPolicyMetadata},
+		{simulation.WeightMsgLeaveGroup, group.MsgLeaveGroup{}.Route(), simulation.TypeMsgLeaveGroup},
 	}
 
 	for i, w := range weightedOps {