Origins
The word 'have' is the second most common verb in English (after 'be'), serving both as a main verb expressing possession and as an auxiliary forming the perfect tenses ('I have gone,' 'she has seen'). It descends from Old English 'habban' (to have, to hold, to possess), from Proto-Germanic *habjaną (to have, to hold, to lift), from PIE *keh₂p- (to grasp, to seize).
The connection between 'have' and PIE *keh₂p- is mediated by Grimm's Law, the systematic sound shift that distinguishes Germanic from the other Indo-European branches. PIE *k became Proto-Germanic *h, and PIE *p was preserved, yielding *hab- from *kap-. The same root without the Germanic sound shift produced Latin 'capere' (to take, to seize, to grasp), one of the most productive Latin verbs in English vocabulary. From 'capere' come 'capture' (to seize), 'capable' (able to take hold), 'capacity' (ability to contain — how much can be grasped), 'captive' (one who is seized), 'accept' (to take toward oneself), 'receive' (to take back), 'perceive' (to take thoroughly — to grasp with the mind), 'deceive' (to take away from — to trick), 'concept' (something taken together — a grasping with the mind), 'recipe' (take! — the imperative of 'recipere'), and 'prince' (one who takes first — primus + capere).
The semantic shift from 'seize' to 'possess' occurred within Proto-Germanic. The original sense of *keh₂p- was dynamic — an act of grasping or snatching — but the Germanic reflex *habjaną had already shifted to static possession by the time of the earliest records. Old English 'habban' never means 'to seize' — it always means 'to hold, to possess, to keep.' The dynamic sense was offloaded to other verbs ('take,' 'seize,' 'grab'), leaving 'have' as the default expression of possession.
Latin Roots
The auxiliary use of 'have' to form perfect tenses ('I have eaten') developed from a possessive construction. The original pattern was 'I have the letter written' — meaning 'I possess a letter that has been written.' Over time, the object was reanalyzed as the object of the participle rather than of 'have,' and 'have' became a pure tense marker with no possessive meaning. This grammaticalization process occurred independently in most Germanic and Romance languages — German 'ich habe gegessen,' French 'j'ai mangé,' Italian 'ho mangiato' all show the same 'have + past participle' perfect construction.
The word 'behave' is a compound of 'be-' + 'have,' originally meaning 'to have oneself, to hold oneself, to conduct oneself.' The 'have' in 'behave' preserves the older sense of 'hold' rather than 'possess.' Similarly, 'haven' (a harbor) is from Old English 'hæfen,' related to 'have' in the sense of 'a holding place, a place that holds ships.' 'Heaven,' despite the phonological similarity, is probably unrelated.