Do other dogs frequently come to your house? Your westie could be feeling like his territory is being invaded, and since they are both males he could feel threatened. He is clearly not being accepting of your new puppy into the pack. This could be a matter of waiting and letting your puppy fall into his place in the social hierarchy. You could start separating them and slowly introducing the puppy, and rewarding your Westie for calm behavior. But mainly I think this is a time matter.