I broke the 2nd & 3rd metatarsal 4 years ago and from my experience the quickest way to heal is to start putting some weight on it as soon as you can, in one of those support boots if you have one,then elevate it above your heart when you chilling. After 5 weeks it was good to go. Was difficult getting it in my ski boot for the first time but once it's in it feels soo good, nice and compressed.
If you go on some online forums for broken metatarsals you will see the people who do no weight bearing for 6 weeks + all saying that it's taken them 2-3 months or more to heal.
However I'm not a doctor, just speaking from personal experience.