The headlines read that obesity increases the risk of cancer recurrence and death in women who are diagnosed with breast cancer.  The actual study involved an evaluation of several groups of women who had stage 1, 2 or 3 breast cancer and were themselves enrolled in clinical research trails.  The purpose of those research trials was not to determine if weight impacted recurrence or mortality, but to evaluate the efficacy of new chemotherapy drugs.  This is important.  Who were the women in the sample, how much are you like them, and how much are other breast cancer patients like them?
    The women who were studied all received chemotherapy and had operable cancers (I do not know if they had surgery, only that they had operable tumors and received chemotherapy).  A consideration to make is whether or not the people who chose to enroll in the study are different from people who did not enroll.  Also, only certain types of people were allowed to participate.  Usually, and it is true here, the people in drug studies have the condition the drug is trying to treat, but are usually otherwise healthy.  This study left out people with "significant" co-morbidities (other diseases occurring at the same time), but I do not know what 'significant' includes.
   The headlines refer to BMI as the risk factor, but having a BMI of 30 or higher isn't the problem.  What that number might reflect is the problem.  For most people BMI mirrors waist circumference (WC) - they mean the same thing.  However, in some people the BMI does not reflect their weight status well.  Waist circumference over 35 inches or higher is a very good indicator that a person also has insulin resistance, high triglycerides and high blood pressure.  It is those issues - collectively called 'metabolic dysfunction', that puts people at greater risk of disease and death.  Consider that those conditions; high blood pressure, trouble with sugar, high blood fats,  make the body less robust, less able to fight off infection, less able to rebound from injury and disease.  Metabolic dysfunction is deconditioning and a person with these conditions (including a WC 35+ and a high BMI) is at a disadvantage before treatment for cancer ever begins.
   This way, obesity and smoking are similar - both increase the risk of disease and death from any disease - just know that BMI and obesity are not the cause - it is the metabolic dysfunction.  Maybe they are the cause of the cause.
    Here is a link to the study regarding the outcomes of the 3 drug trials that were used for the headline making stories.

Study reference:
 Sparano, J. A., Wang, M., Zhao, F., Stearns, V., Martino, S., Ligibel, J. A., Perez, E. A., Saphner, T., Wolff, A. C., Sledge, G. W., Wood, W. C., Fetting, J. and Davidson, N. E. (2012), Obesity at diagnosis is associated with inferior outcomes in hormone receptor-positive operable breast cancer. Cancer.