This popular science piece outlines some of the evidence for greater height to come with a penalty to longevity. I believe that the most plausible contribution to this effect has to do with growth hormone metabolism, given the degree to which it is linked to longevity in laboratory animals. Broadly speaking less growth hormone means a longer life in species such as mice. Larger individuals with more growth hormone accumulate damage and dysfunction at a faster pace in all areas: they age more rapidly.
One of the goals for future medicine is to make all such correlations in long term health irrelevant. Advanced medical technology, sufficient to repair the causes of aging, will sweep away the effects of differences in genetics and circumstances. This is something to look forward, as with suitable levels of funding and support the first of these new therapies of rejuvenation might be developed and rolled out by the late 2030s.
Physicians and epidemiologists began studying the link between height and longevity more than a century ago. Early researchers believed that tall people lived longer, [but] in fact in the early 20th century height was [a] reflection of better nutrition and hygiene, which increased longevity. Once the studies were limited to otherwise homogeneous populations, a consensus emerged that short people are longer-lived.
Among Sardinian soldiers who reach the age of 70, for example, those below approximately 5-foot-4 live two years longer than their taller brothers-in-arms. A study of more than 2,600 elite Finnish athletes showed that cross-country skiers were 6 inches shorter and lived nearly seven years longer than basketball players. Average height in European countries closely correlates to the rate of death from heart disease. Swedes and Norwegians, who average about 5-foot-10, have more than twice as many cardiac deaths per 100,000 as the Spaniards and Portuguese, who have an average height just north of 5-foot-5. Tall people rarely live exceptionally long lives. Japanese people who reach 100 are 4 inches shorter, on average, than those who are 75. The countries in the taller half of Europe have 48 centenarians per million, compared to 77 per million in the shorter half of the continent.
Setting aside simple mortality, individual diseases are also more common among tall people. American women above 5-foot-6 suffer recurrent blood clots at a higher rate. Among civil servants in London, taller people have been shown to suffer from more respiratory and cardiovascular illness. And then there's cancer. Height is associated with greater risk for most kinds of cancer, except for smoking-induced malignancies.
Unlike intelligence, which has a merely coincidental relationship with height, there are plausible biological explanations for why short people live longer. Researchers have found that the lungs of taller people don't function as efficiently, relative to their bodies' demands, as those of short people. Explanations for the link between height and other disorders are slightly more speculative, but largely credible. Tall people have more cells, which may increase the chances that some of them will mutate and lead to cancer. The hormones involved in rapid growth may also play a role in cancer development. It's even possible that the foods that lead to fast growth during childhood may increase the likelihood that a person will eventually develop cancer. The link between height and clots probably has to do with the length and weight of the columns of blood that travel between the heart and the body's extremities.