The knees and hip joints are the most commonly affected joints due to arthritis.
There are different types of arthritis among which osteoarthritis is more likely to affect these weight-bearing joints.
Osteoarthritis occurs due to the damage to the joint tissues due to pressure exerted on them and wear and tear during routine activities resulting in pain, swelling, and restricted movements.
Being taller or shorter does not seem to be directly linked to the higher risk of developing osteoarthritis in the knees and hips. However, some research studies have revealed genetic links and other factors that might contribute to the inflammation and damage to the joints. This might make you more prone to develop osteoarthritis in an indirect manner.
Let us have a look at the genetic and other factors linked to the height of a person that could make him or her more prone to develop knee pains.
The role of weight
It is known that being overweight can increase the chances of getting osteoarthritis. The weight exerted on the knee and hip joints is more in obese people.
Due to this, the bones and joint tissues are subjected to faster wear and tear as a result of which there can be severe damage to the joints causing pain. This indicates why taller people might have a higher risk of osteoarthritis.
Taller people also have a higher body weight compared to the shorter people of the same BMI (Body mass index).
So, the pressure or weight exerted on their knees and hips while standing, walking, and running would be higher. Day-to-day activities can create more strain on their joints thus accelerating the development of osteoarthritis. This could be a reason why taller people are more likely to complain of pain in the weight-bearing joints like the knees and hips.
However, the primary factor involved here is the weight. It also means that shorter people would also be at risk of osteoarthritis if they are overweight while taller people may not experience any symptoms if they are lean and thin.
The risk reduction in taller people is also possible when they perform muscle strengthening exercises. 
Osteoarthritis in people with less or more than average height
Another research study has pointed out the possible link between the less or more than average height and the development of osteoarthritis.
This study has suggested that people, who are shorter as well as taller than the average height, could have an increased risk of arthritis when compared to people of an average height.
The role of genomes and cartilage
This study has established a new genetic connection between arthritis and human height based on the analysis of 10s of 1000s of genomes proving both extremes of height could be associated with osteoarthritis.
Researchers arrived at these findings by analyzing the genetic makeup of more than 30,000 people in Europe and the US.
They found that people with shorter height have shorter leg bones. So, even the cartilage that makes the joints is less in them. Cartilage provides strength and support to the bones. The reduced amount of cartilage in the bones of shorter people makes them more susceptible to damage thus putting them at risk of osteoarthritis.
Longer bones in taller people
At the same time, taller people have longer bones having heavier weight due to which a higher amount of pressure and damaging stress is exerted on these joints. This is why; even taller people are more likely to develop osteoarthritis. This indicates that both being shorter as well as being taller than the average height could be the risk factor for knee and hip pains.
Since several genes have already been discovered to play a role in controlling the height of a person, this study has suggested that a similar genetic makeup may also contribute to the risk of osteoarthritis.
Other than the genes linked to the height and weight of a person, some other genes have been implicated to be directly responsible for triggering the development of osteoarthritis during this study. 
There have been efforts to explore the genetic link between stature and the risks of arthritis. One research study has specifically shown that common genetic variants associated with arthritis might play a role in human height and vice versa.
This study has confirmed the observations by medical professionals that a connection exists between shorter stature and the increased risk of osteoarthritis.
The variants in the genes that were found to be the most strongly associated with height are located in the region of our genome that is also believed to influence the expression of the genes involved in the development of bones and cartilage in the legs.
This means the genes that decide your height are located close to the genes that decide how well or strong your bones and cartilage would develop.
These genes also determine the length of your bones thereby influencing your height also.
They are believed to work by regulating the secretion of the growth differentiation factor 5, also known as GDF5. Studies have shown that the rare variants in this GDF5 gene could create abnormalities in skeletal development due to which your height would be shorter while your risks of arthritis could increase.
This role of GDF5 has demonstrated why shorter people are at a higher risk of osteoarthritis in the knees and hips. This genetic susceptibility to develop osteoarthritis in the hips and knees in shorter people was found to be more evident in European and Asian populations.
The researchers have proposed that these genetic variants would reduce the production of GDF5 protein due to which the amount of cartilage in the bones would reduce. As a result, the growth of limbs and the angles between joints could vary leading to a modest reduction in the height and increased susceptibility to joint damage and osteoarthritis. 
Risk of injuries in taller people
Another factor that could increase the risk of osteoarthritis is taller people is they are usually injury-prone. Also, injuries tend to be worse in taller people than those experienced by shorter people. Taller people are more likely to lose balance and fall as their body’s center of gravity is located a bit higher from the ground.
The higher incidence of falls can lead to more chances of damage to the joints making taller people prone to develop arthritis.
Impact of injuries
Also, when taller people fall, they are going to go a bit farther, and thus, the impact would be higher.
On the other hand, when a shorter person falls, the distance covered from their original position would be less. And hence, even the impact of the fall would be less. This is one of the reasons why taller people are more likely to have pain in the knees and hips due to injuries and joint damage following injuries. 
This also explains the higher rate of hip fracture in older tall people.