Everyone, (except for the idiot reply from "Mario"), is saying NO, you don't need a full frame. I will agree with you don't NEED it, but it CAN have advantages. First of all, I disagree than the difference in depth of field is a minor thing. For any given aperture, you will have CONSIDERABLY less depth of field with a full frame compared to APS-C. This can work for you or against you. When you have a large group of people to photograph, the APS-C can really be your friend and make it easier to have everyone in focus. On the other hand, any reasonably intelligent bride WILL notice how much better a portrait of her looks with a lovely, soft background compared to things being more in focus.
The full frame can also be a help in low light situations. The full frame camera typically has much better high ISO performance than does a smaller sensor camera. The photosites are larger on the full frame camera, (for any given total megapixel count), and thus do not require as much "gain", (higher ISO), than does a sensor with smaller photosites. A full frame camera with 24 MP WILL have cleaner high ISO photos compared to an APS-C camera with 24MP. (There are exceptions to this. The Canon 5DS and 5DSR bodies are not known for good high ISO performance because they are pushing the limit with the amount of pixels on the sensor and they are thus smaller and more "bunched" together. I personally have a 5DSR and ISO above 1600 is pretty poor).
Lastly, at least as far as Canon is concerned, their very best lenses, (the L lenses), are designed for full frame cameras. I would not say they are "going to waste" when used on an APS-C camera, but they are not truly utilized either. The lenses designed solely for the crop sensor cameras are really not in the same league as the L lenses.
Bottom line is I think that if you are doing well and getting good results with what you have, then stay with it. If you get some bucks up in the future and think you might want to venture into full frame, I would say it can be an advantage to your finished product. Work into it gradually and PRACTICE with any full frame camera you might purchase, because there WILL be some new learning curves you will encounter.
Finally, yes, I have shot many weddings, all with full frame, but I am not saying you cannot do it with crop sensor also. I used full frame because I adopted it very early in my digital conversion from film. I had the first full frame digital DSLR, the Canon 1Ds. From that I went to the 5D MkII and now the 5DSR, though I no longer shoot weddings. I also have some cropped sensor cameras, one of my favorite being the SL2 for it's small size and light weight. Like EVERYTHING in photography, it is always a compromise of one type or another.