I can understand that it would be frustrating initially because you can't "see" the changes you are making taking effect and it will take a few weeks or months to really find it noticeable in measurements - however, you can just trust that you are following a really healthy eating plan that is sustainable for life and try and focus on that, rather than the numbers on a scale, because the rest will follow naturally as a matter of course, if you can't find somewhere to get weighed and you don't like getting weighed anyway.
Within a month or two, you will find your clothes are much easier to get on, so that's one good marker. Find something you find "tight" now, and use that as a guide in terms of how different it looks on you from one month to the next. It's actually quite a positive thing that you can't get weighed, because it is VERY easy to get scale obsessed when following a weight loss plan and your resolve and self-esteem can be shot to ribbons by a sneaky weigh-in that sends you off plan in a sulk. So, at worst, go for the three month weigh ins at the hospital, or maybe ask to weigh monthly at a local nursing home if they have the facilities, OR just trust in the plan and know that you are doing a great thing and the results will become clear over the next few months.