Why a backup created on SQL Server 2016 is significantly larger than one created on SQL Server 2012?
Sometimes your backup device can be bigger in comparison to the previous version for reasons like:


Your transaction log increased, check your log to validate if you have not grown it.
You could have extra features enabled in your new instance that are not in the previous instance. i.e: if you have used Full Text-search in your SQL 2016. One time a customer database backup got exponential growth for this.
Your backup device on the new SQL Server version is not initialized {NON Init | Init} in other words your backup file appends the backup into the same file each time that you performed a backup.

--Media Set Options
  { NOINIT | INIT }
| { NOSKIP | SKIP }
| { NOFORMAT | FORMAT }



More details here.