Your friend is entitled to attend ante-natal appointments without taking annual leave. Is there an occupational health physician or nurse in the bank that she can attend and to whom she can talk about her back and the stairs?
If not she needs to get her own doctor to write asking about same and asking that she be provided with the chair for Health , Safety and Welfare reasons. Equally if she works for a bank there is bound to be a Health and Safety Officer there to whom she could write enclosing a copy of her doctor's recommendations. It is usually not enough to just ask for a special chair as a lot of these large organizations are very bureaucratic and do not want to set precedent without a written reason.However under H/S regs the onus is on the employer to make the workplace safe for all employees so a chair should not be a big problem.
Now the stairs is different . If the employer can, they should, if possible, move her to an office that is more suitable . They may be able to do this easily, but she is not suffering from an illness nor is she disabled. Granted, four flights of stairs first thing is hard, but for the rest of the day, if she is a woman with normal health , exercising up and down stairs six or seven times daily would just be considered good for her. She can go on maternity leave at 30 weeks as far as I know and if she is very large she may have no choice. Sitting down and minding yourself is not the way to ensure a healthy pregnancy; exercise and keeping a firm eye on her weight would be much more beneficial. If she is having health problems as in raised blood pressure etc then she needs to go on sick leave for her own and the baby's sake.