Depends on what you count as expensive. If you're doing the aforementioned backyard barbecue wedding + Target dress, sure, you can do it on the cheap.

If you want to get married in a venue you have to rent and plan to host a dinner/dance, then you are going to spend a couple grand at least. Not all weddings are $20,000+, but even cheaper weddings are going to be somewhat expensive. But then, I also don't think it's particularly weird to put a little money into hosting a nice party for a very special event.