When I set up my first swift ring, to add the node it was as simple as calling:

$export ZONE=1
$export STORAGE_LOCAL_NET_IP=192.168.0.4
$swift-ring-builder account.builder add z$ZONE-$STORAGE_LOCAL_NET_IP:6002/$DEVICE $WEIGHT
WARNING: No region specified for z1-192.168.0.4:6002/sdb1. Defaulting to region 1.
Device d1r1z1-192.168.0.4:6002R192.168.0.4:6002/sdb1_"" with 100.0 weight got id 1

However, if I set the weight to zero, and then remove the node the same way:

$swift-ring-builder account.builder set_weight z$ZONE-$STORAGE_LOCAL_NET_IP:6002/$DEVICE 0
d1r1z1-192.168.0.4:6002R192.168.0.4:6002/sdb1_"" weight set to 0.0
$swift-ring-builder account.builder remove z$ZONE-$STORAGE_LOCAL_NET_IP:6002/$DEVICE
d1r1z1-192.168.0.4:6001R192.168.0.4:6001/sdb1_"" marked for removal and will be removed next rebalance.

Then I add the node again - this time with a different zone:

$export ZONE=2
$swift-ring-builder account.builder add z$ZONE-$STORAGE_LOCAL_NET_IP:6002/$DEVICE $WEIGHT
WARNING: No region specified for z2-192.168.0.4:6002/sdb1. Defaulting to region 1.
Device d1r1z2-192.168.0.4:6002R192.168.0.4:6002/sdb1_"" with 100.0 weight got id 1

Then wait the allotted period (1 hour) and rebalance:

$sudo swift-ring-builder account.builder rebalance

I get:

Reassigned 262144 (100.00%) partitions. Balance is now 100.00.
-------------------------------------------------------------------------------
NOTE: Balance of 100.00 indicates you should push this 
      ring, wait at least 1 hours, and rebalance/repush.
-------------------------------------------------------------------------------

"repush" isn't in man swift-ring-builder.

At first, swift-ring-builder told me that the relationship was 200.00 to -100.00. e.g.

$ swift-ring-builder /etc/swift/account.builder 
/etc/swift/account.builder, build version 11
262144 partitions, 3.000000 replicas, 1 regions, 1 zones, 3 devices, 200.00 balance
The minimum number of hours before a partition can be reassigned is 1
Devices:    id  region  zone      ip address  port  replication ip  replication port      name weight partitions balance meta
             0       1     1     192.168.0.3  6002     192.168.0.3              6002      sdb1 100.00     786432  200.00 
             1       1     1     192.168.0.4  6002     192.168.0.4              6002      sdb1 100.00          0 -100.00 
             2       1     1     192.168.0.5  6002     192.168.0.5              6002      sdb1 100.00          0 -100.00

Then, after a few minutes, it rebalanced it to 100 to -50:

$ swift-ring-builder /etc/swift/account.builder 
/etc/swift/account.builder, build version 12
262144 partitions, 3.000000 replicas, 1 regions, 1 zones, 3 devices, 100.00 balance
The minimum number of hours before a partition can be reassigned is 1
Devices:    id  region  zone      ip address  port  replication ip  replication port      name weight partitions balance meta
         0       1     1     192.168.0.3  6002     192.168.0.3              6002      sdb1 100.00     524288  100.00 
         1       1     1     192.168.0.4  6002     192.168.0.4              6002      sdb1 100.00     131072  -50.00 
         2       1     1     192.168.0.5  6002     192.168.0.5              6002      sdb1 100.00     131072  -50.00 ...