You should expect the table to grow because the DocStreams table contains all the BLOBs starting with SP2010, whereas in SP2007 they were split between AllDocStreams and AllDocVersions.
If you did your migration/upgrade in place, the Content column from AllDocVersions should be dropped and you can reclaim that space by cleaning up the table (DBCC CLEANTABLE) and shrinking the database (DBCC SHRINKDATABASE) through T-SQL or the SQL Management Studio.
If you migrated your 2007 farm to a new 2013 farm then again, you should still expect the table to be larger in 2013 than 2007, especially if you are storing a lot of document versions. If you see a substantial difference in size between AllDocStreams+AllDocVersions in 2007 and DocStreams in 2013 then you may have a problem.
Beyond that, you'll need to look at RBS to offload the BLOBs and store them directly on your SAN or NAS.