The only reason for a weighted vest (unless training to run an event wearing a heavy costume or rucksack) is to do strength work. They can be great if you are wanting to increase the resistence when doing lunges, squats etc and are a good alternative to hand weights in this situation.
Weighted jackets are uncomfortable to run in because that's not what they are designed for. They bounce and chafe all over the place. My PT has got me running very short distances (maybe 20-50m) when we have done sessions outside in the cold in winter. In this case she is getting me to run to warm me up when the air tempertaure is low, and not as running training specifically.
