I learned that age is mutations across cells that become more common as you get older. Since a bigger person uses more calories and their cells die and are renewed more often, does that mean they have more mutations and age faster than normal?
What you mean by "big people"? Obese? Very tall but not obese (BMI in proper range)?
My answer for obese: probably they do age faster, but this is not so easy to prove as we lack measurement tools to measure aging intself. Quote from Obesity accelerates epigenetic aging of human liver (2014):
Because obese people are at an increased risk of many age-related diseases, it is a plausible hypothesis that obesity increases the biological age of some tissues and cell types. However, it has been difficult to detect such an accelerated aging effect because it is unclear how to measure tissue age. Here we use a recently developed biomarker of aging (known as “epigenetic clock”) to study the relationship between epigenetic age and obesity in several human tissues. We report an unexpectedly strong correlation between high body mass index and the epigenetic age of liver tissue. This finding may explain why obese people suffer from the early onset of many age-related pathologies, including liver cancer.
Assessing tissue age poses a significant methodological challenge because it is not clear which biomarkers of aging are appropriate. There is a considerable debate in the literature as to what extent markers/causes of cellular senescence, such as telomere length, capture all aspects of tissue aging (8–10).
If you accept such biomarkers as telomere length:
Leukocyte telomere length, which is a widely used biomarker of aging, has been found to be negatively correlated with body mass index (BMI) (3–7). Although the observed correlation between BMI and telomere length is relatively weak (r = 0.12) (4), it is remarkable that these studies demonstrated that BMI is associated with an age acceleration effect in blood.
Accordingly, understanding the interplay between accelerated ageing related to obesity and adipose tissue dysfunction is critical to gain insight into the ageing process in general as well as into the pathophysiology of obesity and other related conditions. Here we postulate the concept of 'adipaging' to illustrate the common links between ageing and obesity and the fact that, to a great extent, obese adults are prematurely aged individuals.