Does the brain consume more energy when a person is stressed or anxious
The tiredness associated with depression/stress is not due to the 'brain power' increasing but due to a change in what parts of the brain are active and/or disrupted sleep. Anxiety can cause issues to the brain and body over time.
Brain power is relatively constant
For the average adult in resting state the brain consumes about 20% of the body's energy. It has been shown that the brain requires about as much energy at night when you are asleep as during the day. The increase of energy for 'hard thinking' is about 8% which is very little compared to the baseline usage (leg muscles can have a 300-400% increase when walking compared to sitting).
See this paper for more analysis.
Tiredness and Mental Health
Depression affects neurotransmitters associated with alertness and reward systems thus making you feel less awake, less motivated, and more tired even if you might have sufficient sleep. However depression and anxiety often also lead to disrupted sleep (trouble falling asleep, nightmares/poor quality sleep, waking up too early etc). This would lead to a feeling of constant fatigue. Unfortunately, the feeling of fatigue can also worsen feelings of depression and anxiety though it is often not the root cause of depression.
Effects of Anxiety Over Time
Repeated activation of the stress response (a cascade of stress hormones colloquially known as the 'fight-or-flight' response) takes a toll on the body. Research suggests that chronic stress contributes to high blood pressure, cardiovascular disease, and causes brain changes (including differences in the volume of gray matter versus white matter, as well as the size and connectivity of the amygdala paper) that may contribute to anxiety, depression, and addiction. Preliminary research also suggests that chronic stress may also contribute to obesity, both through direct mechanisms (causing people to eat more) or indirectly (decreasing sleep and exercise). Chronic stress keeps levels of cortisol in the body high.
Source
Another important factor is the effect of stress on the cortisol levels.
Stress leads to an increased release of the steroid hormon cortisol, which can lead to reduced bone formation, favoring long-term development of osteoporosis (progressive bone disease) source.
It transports potassium out of cells in exchange for an equal number of sodium ions. This can trigger the hyperkalemia of metabolic shock from surgery. Cortisol also reduces calcium absorption in the intestine source. Cortisol down-regulates the synthesis of collagen source.
Sustained stress can lead to high levels of circulating cortisol (regarded as one of the more important of the several &quot;stress hormones&quot;). Such levels may result in an allostatic load,which can lead to various physical modifications in the body's regulatory networks source.