You can absolutely adopt as a single woman, I am a single adopive mother of 3
If you are overweight as Italian says you will be encouraged to lose weight, but what counts as 'too obese' depends on the individual agency and on what your doctor says in your adoption medical. Some people are accepted to adopt with very high BMI's.
However at 25 you are very young in adoption terms, the average age is I think 38. I was also very young in adoption terms (28) when I applied (and 30 when my first child came home) and I did face some questions about my age. I think you will definitely be asked serious questions about your age. The kind of things social services will be thinking are - if you are able to concieve, you still have lots of time, so why adopt at this point? You could be accepted to adopt and then meet a new partner and then want to have a baby with them. How many of your personal goals have you achieved at this age (career wise, travelling etc etc) and would it be better to wait a few years and spend more time focusing on you before adding a child? If you waited a few years, wouldn't you have gained more life experience, wisdom and things that will be useful to you in parenting?
I am not trying to be horrid at all, but social services can be quite blunt about it, and they do tend to prefer adopters aged 30+ so if you seriously feel that now is the right time to try and apply, then you really need robust and good answers to their questions. You still may find that some agencies would say 'not now, but we invite you to reapply in a few years time and we could take you on then'.
When I attended my first preparation group I was surrounded by married couples aged about 33-45 and I felt out of place as a young single woman - like being the only teen mum in a baby group of older mothers is the closest comparison I can think of!
Personally, at the time I was 28 I did feel I was done with travelling, having short relationships and studying, and I did want a child more than anything else there was for me to persue. BUT with hindsight, I am glad now I did not bring a child home at younger than 30. I think extra age does make a difference in parenting. The majority of adopted children, having suffered trauma and abuse, do have some additional needs, and parenting can be very hard and stressful. If your friends are still childless, then you move away from their company and toward other (usually older) parents. Especially when it comes to adoptive parents, when you network or talk with with adopters you are going to find yourself one of, or probably the youngest person.
I just would advise serious thinking and some caution before moving forwards. Being a young adoptive mum has had some benefits for me, but quite a lot of challenges too, and in addition becoming a parent when I did very much seperated me from most of my friends and acquaintances so I had to find new company from scratch as well.