The largest size of the next block is limited to 2x the median size of last 100 blocks. Creating a block this large imposes a penalty equal to the block subsidy, so the miners entire revenue would have to come from transactions, thus the transaction fees would have to be at least as large as the block reward to entice the miner.
Realistically, a miner would only mine the larger blocks for more money, not just the block reward, so let's assume that you'd need to pay 2 x the block reward in fees to incentivize miners.
The current block reward stands @ 5.5 XMR (https://www.whattomine~5.com/coins/101-xmr-cryptonight5 XMR) per minute, or ~11 XMR per block. Under our assumption, the attacker would need to pay 11 XMR every 2 minutes (block time) to get his ever increasing blocks. With 200k XMR, he could keep this up for about 18,000 blocks, or 25 days.
Based on a spam attack in 2014, a day is enough for that limit to double, so we're looking at blocks that would be about 25x as large by the end of the attack.
In my opinion, 25x is purely theoretical because we would never approach that since there are multiple costs/incentives at play that change as the blocks grow ever larger and the block reward gets pushed off.
First you have the storage of the penalty XMRs waiting to be paid out to a miner that mines a smaller block (I'm not super fluent on the penalty payout, so someone please correct me if I have this wrong). Then you have the increasing CONOP that comes with larger blocks, which will incentivize miners to require even more then 2x the block reward to mine another larger block. All of this acts to effectively reduce the time of the attack. I'm not sure how the numbers all break down, but I'm relatively certain that the incentives are such for all involved that there wouldn't be this death spiral to infinity GB blocks.
Edit: if the penalty is cumulative then the attack time shrinks significantly since the attacker would need to pay more than the accumulating reward every block to keep up the attack.
Also, once the attacker runs out of money, the block size would come back down (adaptive block sizes are awesome).