Good locks seem awfully heavy
The lightest lock I have found which I see as "strong enough" is the Abus 401 d-lock, which weighs in at approximately 1kg. Might that be light enough for you?

Now, when I say "strong enough", what I actually mean is that this lock has a "Sold Secure Gold" rating - this is a scheme used by the UK insurance industry, which basically means that if I attach my bike to something using this lock and the bike is subsequently stolen, then my insurance company will cough up. As far as I am aware this is the lightest lock to meet this standard, and I know of no lightweight chain that I would consider appropriate.

As far as I am concerned bike locks have two purposes. First, to deter. Second, to make sure the insurance company pays out should the worst happen. They will not prevent.

Now having said that I almost never use this lock. This is because when I am out on a leisure ride, I hardly ever park the bike up. If I know I'm going to make a stop, or if I'm touring, I will carry this lock, but not otherwise.

When my bikes are at home, they're secured by (insurance approved) anchors to the garage floor by those heavy chains and d-locks that you've already discovered (in general I like the Kryptonite Fahgeddaboutit range which will deter and are insurance approved). But those locks live in the garage and don't travel.

When I am commuting, I keep a set of locks at each end. Works out expensive but as you say, they're heavy. 

And yes, I mix a chain and a d-lock, both conforming to this Sold Secure Gold standard.

Note lastly that I make absolutely no claim that "Sold Secure Gold" locks are any good at what they do! In fact I've heard others say that its just a scam. But they keep the insurance company happy, that's all.