Wouter,
In the cloud portal under the monitor tab and then trends you can review the database size. The size of specific tables can't be seen directly, for this you could create a backup and restore this locally. Then perform some queries on the database to get the size of the tables, have a look at :
http://www.quantprinciple.com/invest/index.php/docs/tipsandtricks/postgres_commands/tablesize/
and
https://wiki-bsse.ethz.ch/display/ITDOC/Check+size+of+tables+and+objects+in+PostgreSQL+database