If you said "กระเป๋านี้หนัก" you said without any classifier
But "กระเป๋าใบนี้หนัก" "ใบ" is the classifier of the bag. Also "ใบ" can use with leaf , papar (some use แผ่น) , bag,
You can use with or without in routine talking. Because sometime I didn't tell how much of things I want I just say without any classifier.
เขามี 2 บ้าน wrong , if you mean he has 2 houses.
บ้าน is not classifier. It's different from English that they used its word to classifier after number.
The correct is เขามีบ้าน2 หลัง "หลัง" is the classifier to บ้าน
It a complicated and need a lot to remember , but don't give up. !