Heathcliff wants Catherine under his control because by forcing her to marry his son who was so weak that he was bound to die sooner or later, Heathcliff would end up getting Thrushcross Grange If so, then Edgar wants to keep her away from Heathcliff because he knows first hand how evil and vindictive Heathcliff can be. Plus he was the 'other guy' in Edgar's relationship with his wife.Cathy is young and naive and Edgar just wants to protect her like any father would. Beside, Edgar knows what heathcliff is capable of after he married Isabella under the guise of love just so that he could eventually get his hands on Edgar’s property after his death because he knew that would piss him off majorly. Also, he treated Isabella like a slave dog and
