There seem to be a lot of possibilities in this situation - and also when you send one text and the person receives two.
As far as I can tell, you need to...
1 - decide on one desktop icon to handle your text messages. If you have two (ex: the text message icon and the mailbox icon), they fetch separately. I don't know if this causes your problem, but mail/contacts on the X is more complicated than it appears. So, if you have only one icon/widget for email and/or texting, life is simpler.
2 - BTW, check your contacts and see how many links there are for each person. I've been doing battle with having increasing numbers of links (many old) for the same person via "phone book" ... and I can't quite identify the source of that entity. I get all my email (incl pop3) through Gmail and sync contacts through Gmail, too. But that's another story...