(1) Have you page compressed any (or better yet all) of the really large tables? And used COMPRESS/DECOMPRESS if it's clob data? [If you're on SQL 2016+ then even Standard Edition has full compression capability. If you're on less than 2016, you'd need Enterprise Edition. I'm pointing that out because I realize that sometimes people post to a higher version than they have because there tends to be more activity on newer-version forums.]
(2) If not, are you using WITH COMPRESSION on the backups? For data not already page compressed, that typically drastically speeds up the BACKUP!
So what should you do first? Use backup compression if not using data compression.
But you really should use page compression if it's available in your SQL version/edition. And, compression or not, you always have the option to move some/most of the tables to other db(s), which you can then back up on different schedules and/or with different methods, as you prefer. Each db would then be smaller than the current combined db, of course.
For example, say you decide to page compress 40% of the tables in the db (you could end up with higher/lower %, but the principle is the same). You might then move the other 60% of tables to another db. But won't that require code changes, which you don't want? No, you don't want to have to change your SQL code, it should continue to work just fine.
To do that, you might, for example, take these steps:
(11) Compress all tables in the maindb that you decide to compress.
(12) Backup the maindb and restore it to, say, maindb2.
(13) Drop the compressed tables from maindb2.
(14) Generate 'CREATE SYNONYM' statements for the non-compressed tables in maindb to point them to the same table names but in the dbmain2 db, like: CREATE SYNONYM dbo.table_name FOR maindb2.dbo.table_name
(15) DROP the non-compressed tables from maindb.
(16) Run the gen'd code in dbmain to create the synonyms for the non-compressed tables pointing to dbmain2, same table name.
(17) From then on, BACKUP dbmain WITH NO_COMPRESSION, BACKUP dbmain2 WITH COMPRESSION.
I realize this isn't necessarily 100% detailed or clear. Thus, if you decide to try this, let me know and I can provide more details as needed.
Note that you can move tables to diff db(s) like above even if you decide not to, or can't, compress any of the tables.
SQL DBA,SQL Server MVP(07, 08, 09) Prosecutor James Blackburn, in closing argument in the Fatal Vision murders trial: "If in the future, you should cry a tear, cry one for them [the murder victims]. If in the future, you should say a prayer, say one for them. And if in the future, you should light a candle, light one for them."