Let us begin by repeating what Vanaga says:

1. Enough, sufficient; ku-rava-á, that's enough, it is sufficient. 2. To be satiated, to be satisfied; ku rava-á te tagata i te kai, the man has eaten his fill. 3. Used very commonly before verbs to express someone much inclined towards this action: tagata rava taûa, quarrelsome person; rava kai, glutton; rava haúru, sleepy-head; rava kî, chatterbox; rava tagi, cry-baby; rava keukeu, hard-working; vara is often used instead of rava. Vanaga.

Rava is here given two main meanings, as I understand it. First of all an intensive, focused, selfish mood, and secondarily the result thereof, viz. enough! The primary sense must be the aggressive mood - hunger in all its senses  - what can be expected after a winter season with scarce resources.
Next we should compare with the not quite so intense and more neutral rave:

Ta.: Rave, to take. Sa.: lavea, to be removed, of a disease. To.: lavea, to bite, to take the hook, as a fish. Fu.: lave, to comprehend, to seize. Niuē: laveaki, to convey. Rar.: rave, to take, to receive. Mgv: rave, to take, to take hold; raveika, fisherman. Ma.: rawe, to take up, to snatch. Ha.: lawe, to take and carry in the hand. Mq.: ave, an expression used when the fishing line is caught in the stones. Churchill 2.

Behind this spectrum of meanings we can discern the idea of 'seize' (to take possession of). In the intensive hungry rava mood much forceful action (rave) must come, must be the result of the primary drives. No time to deliberate or discuss, hunger is ravenous. But rave has no childish tune, it is a calculating and mature 'beast' who is acting.
In Churchill there is much information regarding rava, and we can see that there is no clear bordeline between rava and rave:

1. [I have missed to copy this page in Churchill.] 2. To get, to have, to conquer, to gain, to obtain, invasion, to capture, to procure, to recover, to retrieve, to find, to bring back, to profit, to assist, to participate, to prosper; mea meitaki ka rava, to deserve. PS Pau.: rave, to take. Mgv.: rave, to take, to acquire possession. Ta.: rave, to seize, to receive, to take. To.: lava, to achieve, to obtain. Viti: rawā, to obtain, to accomplish ... 3. To know; rava iu, to discern. 4. Large; hakarava, to enlarge, to augment, to add. PS Sa.: lava, large, very. 5. Hakarava, wide, width, across, to put across, yard of a ship, firm; hakarava hakaturu, quadrangular. P Mgv.: ravatua, the shelving ridge of a road, poles in a thatch roof, a ridge. In the Tongafiti speech this appears only in Maori whakarawa to fasten with a latch of bolt ... 6. A prepositive intensive; rava oho, to take root; rava keukeu, to apply oneself; rava ahere, agile, without fixed abode; rava ki, to prattle; rava vanaga, to prate. Mq.: ava, enough, sufficient. 7. Hakarava, gummy eyes, lippitude. 8. Hakarava omua to come before, precede.

He then continues with words incorporating rava:

Ravagei, to prattle. Ravahaga, capture. Ravaika, to fish. Mgv.: raveika, a fisherman. Mq.: avaika, avaiá, id. Ravakai (ravekai), glutton, insatiable; tae ravekai, frugal. Ravakata (ravakakata), jovial, merry. Ravaki, to prattle, to tell stories, loquacious, narrator, orator, eloquent, to boast, to speak evil, to defame, slander, gossip. Ravapeto, to blab, to speak evil. Ravapure, fervent, earnest. Ravavae, invention. Ravatere, to scare away. Neku ravatotouti, agile. Ravavanaga, loquacious, garrulous, to tell stories, narration.

A negative tense is colouring many of these items (glutton, boast, speak evil, blab etc). Table manners are not high in priority when you are ravenous, and in a competition for scarce resources the noble side is put aside. Furthermore childish behaviour comes to the surface in times of stress.

A special case is the double variant of rave:

Ta.: raverave, a servant, to serve. Ha.: lawelawe, to wait on the table, to serve. Churchill.

When the gods and men of equal rank have sat down to take what they want the more humble men should stand aside as servants, they are the Mercury characters.
Fornander is as always a good source for coming to grips with the meanings of words, and he has recognized the relationship between rava and rave. First rava (lawa):

LAWA, v. Haw., to work out, even to the edge or boundary of a land, i.e., leave none uncultivated, to fill, suffice, be enough.

Sam., lava, be enough, to complete; adj., indeed, very. Tah., rava-i, to suffice. N. Zeal., rava-kore, lit. 'not full', poor. Fiji., rawa, accomplish, obtain, possess.

Sanskr., labh, lambh, to obtain, get, acquire, enjoy, undergo, peform; lábha, acquisition, gain; rabh, to seize, to take.

Lith., loba, the work of each day, gain, labour; lobis, goods, possessions; pra-lobti, become rich; api-lobe, after work, i.e., evening.

A. Pictet refers the Lat. labor, work, to this same family, as well as the Irish lobhar and the Welsh llafur. He also, with Bopp and Benfey, refers the Goth. arbaiths, labour, work, to the Sanskr. rabh = arb, as well as the Anc. Slav., rabu, a servant. Russ., rabota, labour. Gael., airbhe, gain, profit, product.

The modern word 'robot' combines the meanings 'work' and 'servant'. One cannot avoid thinking about the 'slaves' who do the work and those who take the profit. The division between rava and raverave is still in force, and it was also at the base of the Greek culture. Without work there will be no food, but the food can be taken (robbed) by someone tough enough higher up.

And lawe:

LAWE, v. Haw., to carry, bear, take from out of; lawe-lawe, to wait upon, to attend on, serve, to handle, to feel of; adj. pertaining to work.

Tah., rave, to receive, to take, seize, lay hold of; s. work, operation; rave-rave, a servant, attendant.

Rarot., Paum., rave, id. Sam., lave, to be of service; lave-a, to be removed, of a disease; lavea'i, to extricate, to deliver. Fiji., lave, to raise, lift up.

Malg., ma-lafa, to take, seize; rava, pillage, destruction. Sunda., rampok, theft. Mal., rampas, me-rabut, take forcibly. Motu (N. Guinea), law-haia, to take away ...

Greek, λαμβανω, έλαβον, take hold of, seize, receive, obtain; λημμα, income, gain; λαβη, λαβις, grip, handle. Lat., labor, work, activity; perhaps also Laverna, the goddess of gain or profit, the protectress of thieves; rapio, rapax.

Goth., raupjan, to reap, pluck; raubon, to reave, rob. Sax., reafian, take violently. Pers., raftan, to sweep, clean up; robodan, to rob. Lith., ruba, pillage; rûbina, thief.

The Fijian word lave, to raise, lift up, can by association go on to reva. But basically there is no resemblance between raising food or else to superiors (rave) on one hand and lifting up high in order to suspend (reva).