I don't think they will want to weigh you. In my experience they ask what your aim is (weight loss/increase muscle/tone muscle/get more supple etc.) and then how many times a week you think you can come to the gym, for how long etc.
They may do a fitness test, but only so they know your level and so can advise you how to use each machine without completely killing you!!!
They will then, based on the results and what you tell them, give you a personalised program of what to do, which machine, for how long on which level etc.
They are there to HELP you, not to laugh at you. I've been a member of my gym for years now and it is lovely seeing people arriving, very shy and unsure of themselves and within a few months they are transformed and full of confidence.
No one is judging you for your size, more likely they will be silently cheering you on.
Please don't cry. It'll be fine and it's the first step to losing weight (which I think I saw you wanted to do on another thread?)
If they DO ask to weigh you (which would really surprise me) you can refuse you know. It's not legally obligatory! Just tell them that you would rather not be weighed, but that your goal is weight loss and you can measure that at home.