(transitive, psychology) To focus one's emotional energies on someone or something.
1978 [Simon & Schuster], M. Scott Peck, The Road Less Travelled, 2012, Random House (Rider), page 105,
The feeling of love is the emotion that accompanies the experience of cathecting. Cathecting, it will be remembered, is the process by which an object becomes important to us. Once cathected, the object, commonly referred to as a 'love object,' is invested with our energy as if it were part of ourselves, and this relationship between the us and the invested object is called a cathexis.