The original idea of this root was:

grabbing, grasping

On the Germanic side of the family tree, we have  to have and haben, where it shifted toward the “effect” of grabbing something. Words like heave, heavy, heft and hawk have stayed a little closer to the original sense of grabbing.

In the Latin branch of the family tree, we have the verb capere. This verb meant to take, to hold and it (and its cousins) are the ancestors of a multitude of words like capture, catch, perceive, receive, recover and also cop.

Oh and let’s not forget about principal and prince which originally meant “first one to receive”.

Here’s an (incomplete) list of English members of the family:

• to have (“effect of grabbing”) 
• to heave (“grab and lift”)
• heavy (“something big to lift”)
• heft (“where you grab”)
• hawk (“the grabber”)
• accept (“take to you”)
• perceive, perception, … (“grasp from outside”)
• conceive (“take to you” )
• receive, recipe (“take back and hold”)
• deceive (“take elsewhere”)
• except (“take out”)
• emancipate (“remove from grasp” – ex mano)
• capture, captive (“take hold of”)
• chase, catch (“take hold of”)
• cop (“the catcher”)
• cable (“originally: rope to catch with”)
• capacity (“what you can hold”)
• capable (“what you can take on”)
• anticipate (“take in advance”)
• participate (“take part”)
• principle, prince (“take first (prime)”)
• occupy (“take over”)
• municipal (“community taking”)