Run all you want, but nothing changes the shape of your body like lifting does. I haven't lifted in a long time. Mostly, I don't love doing it. And it always seems as though I can burn more calories doing aerobic exercise. Sure, sure, there are articles saying that if you add muscle, you will burn more calories at rest than if you don't add muscle. But there are articles that point out that you'd have to add A LOT of muscle for that to make a big difference in your metabolism. But there are benefits.
One is to maintain the muscle you have. It's easy to lose muscle if you are losing weight. This is partly because your body doesn't need muscle to support fat that goes away. Part of it is that if you eat too little, your body will consume muscle faster than fat, because it requires a lot of care and feeding, and fat does not. (Shock, right?)
But lifting sure makes everything hang better. My clothes are looser, even though I'm not down much. I mix it up, and I like about a 15 or 20 minute warm up on the elliptical before I lift. Then another 25 or so minutes of lifting. I am getting stronger (I'm keeping track). And it feels as though I've done something, which I like. But the clothes!
So, follow the experts' advice. Do some lifting. You won't get huge (unless you want to, and that takes work). But you will look better. I heard this: Be thin to look good in clothes. Be strong to look good naked.