We have been monitoring some SQLServer: Memory Manager's metrics, and
noticed that after DBCC CheckDB job, metric
Database Cache Memory (KB) drops down significantly. If to be exact,
it dropped from 140 GB cached DB memory to 60 GB
This is correct, you can clearly see this behaviour when this example DBCC CHECKDB command completes at 21h45

Why
This behaviour is due to the database snapshot created by the DBCC command being dropped, removing all of its objects in memory.
You can replicate the behaviour by creating a snapshot of a database, loading some data in memory, and then dropping that snapshot
CREATE DATABASE MY_DATABASE
GO
USE MY_DATABASE
GO
CREATE TABLE dbo.bla(id int identity(1,1) PRIMARY KEY NOT NULL,
val int,
val2 char(100));
INSERT INTO dbo.bla(val,val2)
SELECT ROW_NUMBER() OVER (ORDER BY (SELECT NULL)),'bla'
FROM master..spt_values spt
CROSS APPLY master..spt_values spt2;
GO
CREATE DATABASE MY_DATABASE_SNAPSHOT
ON
(
NAME ='MY_DATABASE',
FILENAME ='D:\DATA\MY_DATABASE.ss'
)
AS SNAPSHOT OF MY_DATABASE;
GO
USE MY_DATABASE_SNAPSHOT
GO
SELECT * FROM dbo.bla;
SELECT
COUNT(file_id) * 8/1024.0 AS BufferSizeInMB
FROM sys.dm_os_buffer_descriptors;
BufferSize before dropping the snapshot
BufferSizeInMB
1061.70312 --before
Dropping the snapshot
USE master
GO
DROP DATABASE MY_DATABASE_SNAPSHOT ;
BufferSize after dropping the snapshot
BufferSizeInMB
824.179687 --after
Second question is why "buffer cache hit ratio" did not change after
DBCC CheckDB completes ?
This depends on how fast the data is loaded back in your buffer cache.
If your buffer pool fills up over a longer time, it should amount to this ratio staying higher on average.
This corresponds with this part of your question:
... It (Buffer pool datasize) dropped from 140 GB cached DB memory to
60 GB. and after that, slowly ramp up again during the week...