Tights aren't particularly light. If you are going to wear them alone, the weight would be comparable to nylon pants.
Running tights may have features like pockets that bring the weight up. They are typically thicker and warmer than light long johns and have more abrasion resistance, being designed to use as outerwear. A pair of large New balance tights are 8.6oz vs silk weight polyester long johns at 5.4oz. And that's not an apples and apples comparison--- I would equate tights with something like Cap 4 for warmth. Power Stretch bottoms are more like 10oz and much warmer, if used with a shell or for sleep.
I would vote for tights for weight/warmth/versatility if worn as an outer layer. I would go with polyester long johns if layering with pants or shells.