I don's understand what you mean when you talk about 'faking chainweight'. If you have a heavier chainweight, your chain is the 'real' chain by definition. What is your definition of a 'fake chain'?
With "faking chainweight" I mean the chain-weight of a chain that includes an alternative transaction as a consequence of a double spend (long-range attack).
The mechanism in detail:
1) the attacker buys, mines and/or lends a large number of coins - he must calculate the approximate number of coins that are staking, and buy more than 50% of them (e.g. 15%+ of the total supply if 30% are continuously "staking")
2) He deposits the coins on a wallet (or various wallets), still without trying to "stake".
3) After some blocks he sells the coins again (this procedure can take as long as he wants if there is no reorg limit).
4) At the same block height he transferred the coins to the exchange, he (secretly) issues a double spend to a wallet he owns and disconnects his client from the network.
5) He then secretly mints an attack chain that contains this double spend (without publishing it). This attack chain would have more chain-weight than the "normal best chain": From the point of view of his wallet/client he still owns the coins and so he can use them to stake, and as
in his attack chain he owns more coins than the rest of the stakers, the weight of the chain is higher.
6) When he has sold all coins (step 3 accomplished) then he publishes the attack chain - it would have more chain-weight than the "true" chain but as we have seen the weight is "faked" using the double spend.
If what you said in the previous post is true and all nodes - including the checkpoint node - always follow the chain with most weight, step 6 would lead to a re-organization on all nodes that obey the protocol and eventually all of them would follow the attack chain. The attack would have succeeded. If the attacker specifically tries to connect to the checkpoint node, then his attack would probably succeed even faster.
I know this attack is very expensive, but the attacker can design it in a way he can profit from it (e.g. if he manages to drive the price higher before he sells). And if he is very likely to succeed, then the incentive is high for a rich individual or group to try it.