Although repetitive DNA forms much of the human genome, its study is challenging due to limitations in assembly and alignment of repetitive short-reads. We have deployed k-Seek, software that detects tandem repeats embedded in single reads, on 2,504 human genomes from the 1,000 Genomes Project to quantify the variation and abundance of simple satellites (repeat units <20 bp). We find that the ancestral monomer of Human Satellite 3 makes up the largest portion of simple satellite content in humans (mean of ∼8 Mb). We discovered ∼50,000 rare tandem repeats that are not detected in the T2T-CHM13v2.0 assembly, including undescribed variants of telomericand pericentromeric repeats. We find broad homogeneity of the most abundant repeats across populations, except for AG-rich repeats which are more abundant in African individuals. We also find cliques of highly similar AG- and AT-rich satellites that are interspersed and form higher-order structures that covary in copy number across individuals, likely through concerted amplification via unequal exchange. Finally, we use pericentromeric polymorphisms to estimate centromeric genetic relatedness between individuals and find a strong predictive relationship between centromeric lineages and pericentromeric simple satellite abundances. In particular, ancestral monomers of Human Satellite 2 and Human Satellite 3 abundances correlate with clusters of centromeric ancestry on chromosome 16 and chromosome 9, with some clusters structured by population. These results provide new descriptions of the population dynamics that underlie the evolution of simple satellites in humans.