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