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Here's what Wikipedia says about this::
It seems to me that a more reliable parameter for establishing the relationship would be the area of the cortex and the ratio of this area to body size, rather than weight or volume per se.
If a person's brain mass is less than about 1 kg, then there is a noticeable positive correlation between brain size and intelligence level. With an increase in brain mass in the range of approximately 1 to 2 kg, average intelligence increases, but very slightly. The minimum and maximum brain size in this interval is considered normal. There is a comparison between Anatole France with a brain weighing about 1 kg and Ivan Turgenev with a brain weighing about 2 kg, both of whom demonstrated quite high intelligence. Brain volume less than a certain amount (for example, the figure of 700 grams is called) is considered a manifestation of microcephaly, which is often accompanied by reduced intelligence. But there are exceptions here, too. For example, according to some sources, the philosopher Hegel had a small brain size.
The weak correlation between brain size above a certain value and the level of intelligence is an argument in favor of the fact that the level of intelligence is mostly determined by social, rather than genetic factors. The observed correlations between heredity and intelligence, which are convenient for justifying social inequality and disadvantage, are not always direct and should be treated critically. For example, there is a point of view that the gemini method can only show the maximum possible influence of heredity on abilities and behavior. Contrary to the stereotype of silly beautiful women, there are significant positive correlations between physical attractiveness and intelligence quotient. They can be explained by the fact that outwardly attractive people are more likely to get a high-quality education and a qualified, high-paying job. Despite the fact that discrimination against women in hiring based on their appearance is stronger, this correlation is stronger for men. This is probably due to the fact that society imposes patriarchal norms on women more strongly in the case of external attractiveness, for example, in the form of a stereotype that one should expect to marry a rich man, and not to be realized in society. But discrimination based on appearance in case of non-compliance with its norms still outweighs on average. In addition, there are stereotypes such as “the appearance of a gopnik” and “the appearance of a professor” and the phenomenon when people try to meet public expectations. That is, heredity can also influence the characteristics of appearance and indirectly through social stereotypes on abilities and behavior. Brain size can also be stereotypically associated with intelligence levels, at least in part, by determining relevant correlations. With a slightly lower average brain size of women compared to men, women have about the same ratio of brain mass to body weight as men, which, according to some data, correlates more with intelligence than absolute brain mass. The higher variation in men's intelligence values can be explained by social factors, when men are more likely to achieve both intelligence-enhancing achievements in society in the face of discrimination against women, and antisocial behavior that contributes to a decrease in intelligence, including due to the fact that such behavior is usually more strongly condemned by women in a gender inequality society.
You should also be critical of the correlations between the average brain size of a particular national or racial group mentioned in the responses and the average level of intelligence. The partially Australoid population of south India has not prevented the recent emergence of a large number of chess grandmasters, including former world champion Anand. The average intelligence quotient strongly depends on education and the chances of getting it in a particular country or for a particular national group. The average IQ of African Americans, although slightly inferior to the average IQ of European-born Americans, is significantly higher than the average IQ of people in Africa, where there are fewer opportunities for education and skilled work than in the United States. The IQ of Hispanic Americans with a predominant European type is close to that of African Americans due to their lower social status as a group compared to English-speaking descendants of Europeans. The minimum and maximum IQ values of different racial and national groups are similar, but the maximum of the sample falls on different IQs, which is also an argument in favor of the social reasons for these differences. The same social reasons associated with discrimination and history, rather than a smaller average brain size, can explain the lower average IQ of the indigenous population of Australia, slightly inferior to the average IQ of the inhabitants of Africa. In addition, intelligence tests often do not take into account the traditional activities of a particular group, and on some tasks such as survival in nature, indigenous peoples show higher intelligence than Europeans.
Recently, human evolution has been associated with a decrease in the average brain size. The brains of modern humans are, on average, somewhat smaller than those of both Neanderthals and Cro-Magnons. This can be explained both by the increased role of social factors in comparison with genetic ones, and by a certain decrease in intelligence in conditions of increased chances of survival. The reduction in average brain size occurs under similar conditions when animals are domesticated. In any case, this shows that we should not neglect the intelligence of the ancestors of people and people from countries and peoples less developed economically. There was a point of view that to make a spear of a Heidelberg man with a slightly smaller average brain size in those conditions was as difficult an intellectual task as it is now to make a nuclear reactor (I don't remember exactly what the comparison was with). Moreover, we should not underestimate the intelligence of Neanderthals with a slightly larger brain size than that of modern humans. However, with the development of education and technology, the average IQ of individual countries is growing, but the average IQ of the world's population is falling due to the higher birth rate in economically less developed countries, where there are fewer chances of obtaining a quality education and skilled work. The position of a group of people in society affects its average intelligence much more strongly than the brain size above the conditional lower limit of the norm.
Canadian-British scientist John Rushton defined the correlation coefficient between cognitive abilities and brain size as 0.44. Yes, the value of the indicator does not seem so significant at first glance, but for comparison: the correlation coefficient between height and weight for US residents is 0.4; between the average grade in high school and the average grade in high school is 0.56