Choose objects by weight. Free license.

gistfile1.js

/**
 * Choose objects by weight.
 * @author Evan Hahn
 * @version 1.00
 * @param {Object[]} objects An array of objects that each have a "weight" property.
 * @param {Number} howMany How many should I choose?
 * @returns An array of chosen objects, containing howMany values.
 * @example
 * chooseByWeight([
 * {
 *     "title": "Apple",
 *     "weight": 4
 * },
 * {
 *     "title": "Banana",
 *     "weight": 1
 * },
 * {
 *     "title": "Coconut",
 *     "weight": 2
 * },
 * {
 *     "title": "Date",
 *     "weight": 1
 * }
 * ], 2);	// Is likely to return the Apple object and then the Coconut object
 */

var chooseByWeight = function(objects, howMany) {

	// Sum the weights
	var totalWeight = 0;
	var i = objects.length;
	while (i --) {
		totalWeight += objects[i].weight;
	}
	
	// Choose from among them
	var chosenOnes = [];
	while (chosenOnes.length < howMany) {
	
		// Pick a random number
		var tryThis = Math.random() * totalWeight;
		
		// Find the one to stop on
		var currentIndex = 0;
		var totalSoFar = 0;
		while (tryThis > totalSoFar) {
			totalSoFar += objects[currentIndex].weight;
			if (tryThis > totalSoFar) {
				currentIndex ++;
			}
		}
		
		// Choose it if it hasn't already been chosen
		if (chosenOnes.indexOf(objects[currentIndex]) === -1) {
			chosenOnes.push(objects[currentIndex]);
		}
	
	}
	
	// Return
	return chosenOnes;

}

There's potentially a big performance issue here, and you're using while loops where for loops should be used instead. Check out my comments here:

https://gist.github.com/47042c834561ba826b2e