First of all make sure backup compression is enabled on the SQL Server. You can execute below query to check the backup compression.
select name,[description],value_in_use from sys.configurations where name like '%backup%'
Execute below script to check the compressed backup file size and backup compression ratio.
Declare @FromDate as datetime -- Specify the from date value set @FromDate = GETDATE() -1 SELECT CONVERT(CHAR(100), SERVERPROPERTY('Servername')) AS SQLServerName, msdb.dbo.backupset.database_name, CASE msdb..backupset.type WHEN 'D' THEN 'Database' WHEN 'L' THEN 'Log' WHEN 'I' THEN 'Differential' END AS backup_type, msdb.dbo.backupset.backup_start_date, msdb.dbo.backupset.backup_finish_date, msdb.dbo.backupset.expiration_date, DATEDIFF (SECOND, msdb.dbo.backupset.backup_start_date, msdb.dbo.backupset.backup_finish_date) 'Backup Elapsed Time (sec)', msdb.dbo.backupset.compressed_backup_size AS 'Compressed Backup Size in KB', (msdb.dbo.backupset.compressed_backup_size/1024/1024) AS 'Compress Backup Size in MB', CONVERT (NUMERIC (20,3), (CONVERT (FLOAT, msdb.dbo.backupset.backup_size) /CONVERT (FLOAT, msdb.dbo.backupset.compressed_backup_size))) 'Compression Ratio', CASE msdb..backupset.type WHEN 'D' THEN 'Database' WHEN 'L' THEN 'Log' END AS backup_type, msdb.dbo.backupset.backup_size, msdb.dbo.backupmediafamily.logical_device_name, msdb.dbo.backupmediafamily.physical_device_name, msdb.dbo.backupset.name AS backupset_name, msdb.dbo.backupset.description FROM msdb.dbo.backupmediafamily INNER JOIN msdb.dbo.backupset ON msdb.dbo.backupmediafamily.media_set_id = msdb.dbo.backupset.media_set_id WHERE CONVERT(datetime, msdb.dbo.backupset.backup_start_date, 102) >= @FromDate AND msdb.dbo.backupset.backup_size > 0 ORDER BY msdb.dbo.backupset.database_name, msdb.dbo.backupset.backup_finish_date