While jogging last week I got caught in a flash rain for about 15 minutes. Jogged through it and after the rain the humidity, thick air, heat and (i'm assuming this is the biggest factor) the extra 5-10 lbs I recieved thanks to soaked clothing made the mile almost impossible. I was dying. And I'm no long distance runner but I can do 2-3 miles and feel better.

So should I start soaking my t-shirts before a run while the weather is still nice? I heard people talk about weight vests/jackets or whatever they're called. Would this accomplish the same goal without a draw back? Just the t-shirt, since soaked shorts might hurt my movement. Figure a 5 pound t-shirt might have a small positive impact?

5 lb shirt? I don't think so, maybe 3 if it's dripping wet...but I think you were tired that day due to the heat and humidity, not the weight of the shirt. There are such things as weighted vests, but you probably don't want to run with them, as they may cause injury when you're bouncing up and down for a few miles.