Is PoS based directly on wealth? I'm not sure of how it works and would appreciate a link related to this.
Proof of Stake means that the greater "stake" a person has (i.e. the greater number of coins), the greater chance of forging the next block and reaping the transaction fees. There are 1 billion NXT and if you own one, you have one chance in one billion to forge the next block. It's not exactly done like that but the result is about the same. Also, if you have a large stake and try to force a fork by not forging a block when you get elected to do so, your forging power drops to zero temporarily which allows others to pickup the slack. Again, I'm a novice at the exact mechanisms of NXT forging.
Keep in mind that you can forge even if you don't own currently one and you owned one in the past by starting at the block before selling. Reorganize the chain and attack the coin