I think, confusing and misleading as the info you've been given has been - and I understand your frustration - you have to remember that the medics do have the health of you and your baby as the absolute top priority here.
As someone whose birth went from fine and dandy in a water pool to full-scale emergency very quickly, I can only vouch for how critical it could be to be in the right place at the right time.
It might be difficult to hear, but the fact is that there are significantly more complications associated with birth when the mother falls into the obese category.
The threshold is there for your safety and, if I were to end up in your position - having had the birth I did with DS - I'd be doing all I could to co-operate with the medics, rather than considering refusing to be weighed etc.
Before I gave birth to DS I was hung up on having the pool, having the birth being midwife-led, no interventions, soft music, low lighting etc. I was in my 20s, a marathon runner, healthy bmi, no other factors that suggested there could have been a problem .
But - and I hate to sound as if I'm scaremongering here - when things go wrong, all that matters is getting out of there safely.
If I were you I'd do some proper research into the risks and make the most informed choice you can as to what you want - apologies if that comes across as patronising and you've already done so.