Probably the first thing that I would recommend that you try is to sign out of iCloud on the iPad, and then sign in again, since it is the iCloud infrastructure that actually transfers messages between devices. You might also want to look into Settings > Messages > Text Message Forwarding on your iPhone, since that is where the iMessage sharing is controlled (i.e., what devices get messages); you may need to turn off the iPad in that setting, and then re-enable it again. Hope this helps... it shouldn't be doing this.
Edit: forgot to include the fact that your iPhone actually controls the sharing of messages, see italics bold.