The extra weight is the inevitable penalty for the keyboard. It surely wasn't a surprise to you?
To be honest, yes the weight was a surprise for me. It is one thing reading about a handset and another thing entirely to hold one. I don't know about where you live, but where I am (at the time I was looking for a new phone last year), you couldn't physically get hold of the Desire Z anywhere.
The additional weight and chunkiness of the phone were a bit of a shock, but I could live with those aspects if it wasn't for the hinge which does make it feel unstable and that is not a good combination.
When I pick up the phone, it frequently gives a little as the hinge moves, even if I am only answering a phone call or moving it around. And contrary to what Stuntman suggested it is very easy to pick it up only by one half of the phone and have it pop open by accident due to the fact it is quite a chunky phone. In fact I would have thought that it takes greater effort to deliberately hold it by both halves every time you pick it up to avoid this.
While it is true that some prefer the easier opening, I would rather have something that more rigid and stable, or at least was fixed in place until you reached a certain point after which it became easier to move.
Then you bought the wrong handset. It happens. Probably best try to sell the Z on and replace it with something you can live with.
Unfortunately I'm probably stuck with the phone and the contract for a while now, so that isn't really an option unless I can sell it close to the price of a new handset - which seems unlikely quite frankly.
Don't get me wrong, I do like the keyboard and the battery life is pretty good for a smart phone ... but I don't like the hinge.
If I had the option (and I have asked) I would swap it for the new HTC Desire S - it doesn't have a keyboard (which is a drawback) but does have battery life similar to the Z.
(Stuntman - yes HTC Merge does look a lot better and I would love to replace the Desire Z with that).