"How will they know what your BMI is? Surely if you are ill enough to need to be ventilated they won't weigh you."
ICU beds have built in scales and a tape measure is used to measure the height. ICU patients are weighed every day because it gives very valuable information about fluid load, nutrition, etc. Some ICU drugs (such as noradrenaline) are given based on actual body weight. Other treatments (such as ventilation volumes) are given based on ideal/expected body weight. You can cause as much damage by over ventilating a patient as by under ventilating them, so it is necessary to be accurate.
I think the key here is to remember that doctors (in this case anaesthetists, as nearly all ICU consultants are actually anaesthetists with specialist training in intensive care medicine) are trained and expert in making these difficult decisions. For example, there are many times when an older person breaks their hip and a decision has to be made about whether to operate. Generally, that comes down to a balancing act and the patient/relatives are told 'If we operate, Harold has a high chance of dying. If we don't operate, Harold will die.' Some patients accept that the odds are against them and refuse surgery, knowing they will die. Others will say 'let's give it a go...'
All treatment is based on the premise of 'doing least harm'. Intensive care is barbaric. It is invasive, causes suffering and can cause psychological damage. It is only justified if there is the prospect of potential recovery. Otherwise, we are just denying a patient a peaceful death. These decisions can be made hour by hour, or even minute by minute. It can be the case that a treatment is justified at 8.30 am and not justified at 11.00 am. That's why there are always twice a day ward rounds in ICU (mandated) and treatment plans are modified as needed.
I really don't think that BMI is something to ponder at this moment. It is what it is and nobody can safely bring themselves from a BMI of 40+ to a BMI of