Define light weight.
The Tikka will come in at 7 lbs scoped. A Kimber will be $400-$500 more, but be about 17-18 oz lighter. The extra money buys a far better stock, and CRF as well as more than a pound weight loss. I like the Tikka very well, but the extra money for the Kimber is worth the difference to me. If I were on a more limited budget and considered 7 lbs light enough, I'd have no problem recommending the Tikka.
You could also pick up a Remngton 700, stock it in an Edge and be right at 7 lbs and within your budget. A Winchester 70 will be about 2-3 oz heavier.
Spot on advice. My Montana is a full pound lighter than either of my Tikkas. I have an Edge-stocked 700 LA with a VX2 that weighs 7lbs, 5 oz. I expect the 700 SA project I am working now will come in close to the same weight with a McSwirly.
