Mostly due to batteries. If you compare the power usage of laptops then, and now, you'll find that older laptops tended to use in the 10-20W range for their motherboard and CPU. Modern ultra books use a similar power level, while modern laptops use around 30-50W, and still get longer battery life.
No, mostly due to higher IPC, agressive power gating and deeper sleep stages. Here's the extended battery pack from my 2002 UltraPortable, 3600 mAh in 330 grams. In 2014 the extended battery for the Sony Vaio Pro 11 is 4690 mAh in 290 grams, that's about a 75% increase in power/gram in 12 years. There have not been any major revolutions in battery technology, it's still the same lithium-ion technology just a little more refined.
You're not comparing just the weight of the energy storage element, but also the weight of the casing. And that has changed a lot in the last 10 years.