From be- (as an intensifier) + the archaic verb long 'belong', based on old english gelang 'at hand, 'together with'.
Belong – 1. be the property of; 2. be a member of (a particular group); 2.1. have an affinity for a specified place or situation; 3. be rightly placed in a specified position.
Longing – 1. a yearning desire.