Very overweight patients have several issues in theatre as do very underweight patients.
For obese patients their surgeries tend to be longer, they need more specialised equipment and more surgeons and assistants just to help with gaining access to the area they're operating on. Positioning is very difficult as you need to make sure there isn't too much pressure on an area which can cause ulceration, we've had to have patients come to theatre weeks before their surgery in order to get them onto the table to see if we can position them safely and securely and organise more equipment if needed. Longer surgeries need longer anaesthetics meaning they're lying on their pressure areas for longer and the longer a wound is left open the higher the infection risk. Due to the nature of certain surgeries it's not always possible to perform pressure care at regular intervals if at all. Longer surgery equals longer recovery and longer stays in hospital plus all the aftercare.
Anaesthetising is more difficult if the anaesthetist can't extend the neck fully, also the amount of weight on their chest means they can desaturate very quickly when lying flat. If access is too difficult/too risky when they're flat then they may need an awake fibre optic intubation which takes longer than an ordinary intubation and is far more traumatic for the patient. If you do get into difficulties which require emergency tracheostomy/cricothryroidotomy it's made even more difficult if there's a lot of neck fat/little space to work on. Even putting in venflons, arterial lines, spinals etc can be very difficult purely because of fat and lines can easily become blocked when positioning.
You also have the other issues which tend to come hand in hand with obesity such as high BP etc.
I don't think surgeries should be declined purely based on BMI, it needs to be looked at on an individual basis. Some patients with a BMI of 30 may not have half of these issues if any so to use something unreliable like BMI wouldn't be fair at all.