While this answer is based off theoretical work that applies strictly to wage labour, the insights presented are also relevant for "petty commodity production," or, the situation where a large peasantry is producing simultaneously for market as personal consumption. Or where Thompson's "plebeians" are in receipt of wages, but not structured as wage labourer (ie: where the wage relationship isn't centrally determinate in their class experience).
Marx strongly asserts that workers consume their entire wage bundle immediately; that the wage bundle is socially determined (by class war, of course) and may fall below subsistence or rise toweringly above it; and that the commodities that make up the wage bundle only have a tenuous link with their embodiment of value (same as the previous, but value centred rather than use centred). This holds true even for savings, which Marx and Engels address in relation to deferred unemployment consumption, or self-pensioning. (The distinction can also be seen later in Volumes II and III in terms of the difference between Departments IIa (consumption by workers, necessities) and IIb (consumption by capitalists, luxuries). Although this division is arbitrary, it is arbitrary on the basis of the difference between wage and profit; the wage being entirely consumed, profit being split between recapitalisation and consumption).
If we proceed from this, to a conception that the peasant consumers of mass sugar were in an imperialist relationship with a prefiguring "factory" and unpaid proletariat in the Americas, this all becomes clear: sugar became cheap on the rent of zero waged slave labour. This is demonstrated in the Autonomist tradition, see Federici (cite follows) at 225, "The tribute which the Spaniards exacted was much higher than that the Aztecs and Incas had ever demanded of those they conquered; but it was still not sufficient to satisfy their needs. By the 1550s, they were finding it difficult to obtain enough labor for the both the obrajes (manufacturing workshops where goods were produced for the international market) and the exploitation of the newly discovered silver and mercury mines, like the legendary one at Potosi." Manufacture of goods on a speculative basis for sale as a commodity was occurring. Thus the "virtuous" cycle of capital reinvestment of the value form could proceed apace in the Americas, with the "degradation" of free labour to wage labour occurring in the middle passage.
Cheap sugar was built on the backs of slaves; but, the reason why recapitalisation happened in sugar was that production was developing on a capitalist basis in the colonies. For more evidence see the position of the Sugar lobby in Britain as a separate lobby from the corn and manufacturers lobby.
Necessity then is the combination of supply (embodying value), and intensification of production as capitalisation (requiring greater realisation to realise the cost of capital, such as slaves), with a willingness to raise the volume and variety of utilities consumed in the metropole while avoiding raising the value composition of the consumed bundle. A similar process occurs later with cotton, or iron work, or iphones.