The entire volume has to be transferred in one piece, sector by sector. Disk Utility can usually do this by creating an interim image, but that requires an even larger disk as a temporary storage medium.
This hint is a bit more low level, but once understood, pretty simple: Copy all volume blocks to the new drive, then adjust the volume's size to match the new, larger, partition. That's it.
In this article I describe how I moved my entire Time Machine backup from one internal disk to another, larger, one. This technique keeps the backup volume intact so that TM keeps using it without the need to start over by losing all previous backups. In my case, I had the volume on a mirrored RAID set, and move it to another, larger, mirrored RAID set - so this works, too.
Warning: This is a hack that requires some technical understanding of disks. Due to the nature of the operation you could, if you are not paying attention, erase the contents of valuable data on your disks. I have made an effort to tell you what to do to avoid such mistakes during this procedure, though.
Note: Usually, this can also be done using Apple's Disk Utility application, by first creating a disk image from the backup volume, then restore that to the new drive. But that requires more steps and another, even larger, interim drive to store the image file, so my solution may actually be less of a hassle.
[crarko adds: I haven't tested this one. If it were me, I'd use Disk Utility as described in this hint. I've had pretty good luck using the 'Restore' option in DU to copy full drives. It also looks like Carbon Copy Cloner can do this.
I put in the link to the article rather than just pasting the contents here. I view it as another method, and the iBored program used looks like a nice little hex editor. As mentioned above, use it with caution. The article provides it bit of a primer on HFS+; for a more in depth look see this Apple tech note.]

