Reconsider a weight. A solution I've used for both my bath fan vent as well as dryer vent is to glue a nut (machine bolt type) as a weight near the lower flap edge. However, my particular dryer run is very short - a few feet, and the bath vent run is no more than 10 feet with a 70cfm fan. The vents run well with very little added back-pressure. I used Goop for glue.
Your oven fan may not have a high cfm, so I'd recommend temporarily taping a smaller nut on first to observe the back-pressure difference while running the fan, and then keep going larger.
Sometimes in the winter if I know a very windy stretch of days are coming, I temporarily screw in a matching machine bolt to my dryer nut, but I don't recommend that unless your memory is good enough to remove it before use.
Also consider a vent like: http://store.heartlandnatural.com/category_s/47.htm with spring kit accessory. I used that for a rental bath vent new installation once with the purpose of keeping critters out. Found vent at Menards and had to order spring kit online. But even with the spring kit, there was more back-pressure than I cared for with a 50cfm bath fan and 15ft run, although still functional.