very generally, anaesthetists are keen to see any woman who may be more complex than average during the antenatal period so that a) we're not having to make plans in a real hurry if an emergency arises and b) women have an opportunity to find out more about the options as applies to them specifically for pain relief/anaesthesia. Having obesity can pose some challenges in pregnancy if a woman needs/wants any intervention from an anaesthetist and it's fairly standard for women with a booking BMI over 40 to be seen by an anaesthetist. Even if a woman's birth plan is a straightforward vaginal delivery with no analgesia we need to have a plan for all possibilities including the emergency scenarios so we can help to safely support them. Things they may go over so they can make these plans with you include: any other medical history (including any history of having anaesthetics/epidurals/spinals in the past), medications (including whether you're on antenatal blood thinners) etc; roughly where someone's weight is distributed (particularly around the lower back or neck); how good your veins look.
For some women we might suggest an early epidural in labour for two reasons: 1) Obesity can make it harder to site an epidural (it definitely doesn't always, but it can sometimes cause problems) and earlier on it's a bit easier to sit still in a good position to get it in, 2) GA at term is higher risk than when not pregnant (which is why we try to avoid it where possible), and this is even more the case when someone has obesity. Having an epidural that's worked well in labour can mean that if an emergency were to arise then that epidural could be topped-up quickly and reduce the chance of needing a GA for eg. a quick c-section. The anaesthetist might examine someone's back and be able to give a rough idea about whether they think getting a needle in the right place would be any trickier than usual and help to weigh up the pros vs. cons of epidurals for labour. If a GA is needed though, having seen a women in the antenatal period means it's possible to plan the safest way to do things (often it doesn't need anything very special to be done differently, but sometimes there is extra kit that is useful at least there's the opportunity to plan for it).
If a woman is taking antenatal blood thinners those need to be stopped for some time before it becomes safe again to do an epidural or spinal injection so if that's the relevant they may give advice about that.
If it looks like someone's veins are terrible, then there may be some advantage to getting a cannula in even if they're planning a low risk vaginal delivery because, again if an emergency arises, then siting a cannula quickly may be even harder.
It's important to know that none of this is about trying to make people feel bad about their weight/persuade them to do one thing or another, but is about making sure women understand the potential problems and can make a properly informed decision and for us it's about spotting where problems might arise and having a plan for managing them. The website labourpains.org has an info sheet re anaesthesia with a raised BMI under the 'during labour' tab.