The Bitcoin blockchain currently has a maximum of about 2 MB per block, or 288 MB per day (6 blocks per hour * 24 hours). Cryptonite's mini-blockchain, as far as I know, saves the transactions of about one week.

So the blockchain would have a static size of about 2 GB (in contrast, Bitcoin's blockchain size is about ~160 GB). This value would only increase if there is a higher transaction density. Additionally there is the proof chain, which is relatively small, but grows over time.

2,x GB is ... almost nothing for today's computers, and the reason why I'm supporting Cryptonite