The GS4 is a fragile phone though. The phone is well built, but I doubt it will take a fall. The galaxy s1, and the s2 was light but can take a beating. I lost count of how many times I dropped my phones and it came back begging for more. People complained and said the original Galaxy S1 and S2 felt cheap and fragile, and I use to defend it because it was still strong as hell.
But the Galaxy S3 is the 4 is very very frail by comparison. I dropped my GS3 twice, and the 2nd time was from 2 feet on to concrete and I broke the screen. My GS1 fell like that about 50 times and was fine, and I ran my GS1 **** naked. I think the problem is that the phones are too damn thin, and that the screen no longer has a bezel to protect the glass. The older Samsung phones, the highest part of the front face of the phone was the plastic bezel, not the glass itself.
Back to the OP, you will eventually get used to the weight and will wonder how you ever carried around such a heavy large brick the whole time. But I would still be very careful not to drop the phone. The phone is well built enough to not fail on its own, but just be careful.