This is a surprisingly difficult and complex question.
Firefighter applicants have been challenging and litigating weight limitations and other physical standards for decades. My very first case as a lawyer was a firefighter weight case against the City of Los Angeles in the 70's, a very long time ago.
But even at this stage of the development of the law, there is no easy answer to this question. Objective physical requirements and qualification standards are lawful if they can be validated as job-related. Validation is an expensive and highly technical analytic process, usually performed by independent experts and statisticians, that measures whether there the standard offers the employer correlation and predictability for effective job performance. Different weights, schemes for implementing the limitation, varying job duties -- all will bear on the legality of a specific standard in a specific jurisdiction.
I know of one case that was decided against the applicant because in a field test the applicant could not fit into a crumpled VW bug and achieve a rescue of an injured "passenger" (dummy bag).
You need to talk with a skilled and experienced local employment discrimination attorney. Look for one that has specific experience against the municipality or governmental entity that controls your FD. Look for an attorney that has litigated "adverse impact hire" cases involving safety positions. You cannot afford to get into a validation case unless there is a contingent fee agreement, but a skilled and experienced litigator who wants your case will make that fee arrangement with you.
Best of luck.
No legal advice here. READ THIS BEFORE you contact me! My responses to questions on Avvo are never intended as legal advice and must not be relied upon as if they were legal advice. I give legal advice ONLY in the course of a formal attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by joint execution of a written agreement for legal services. My law firm does not provide free consultations. Please do not call or write to me with a “few questions” that require me to analyze the specific facts of your history and your license application and prescribe for you how to get a State license. Send me an email to schedule a paid Consultation for that kind of information, direction, and assistance. My law firm presently accepts cases involving State and federal licenses and permits; discipline against State and federal licenses; and disciplinary and academic challenges to universities, colleges, boarding schools, and private schools. We take cases of wrongful termination or employment discrimination only if the claims involve peace officers, universities or colleges.
I agree with Christine's answer but would like to offer a personal note.
In December of 2006 I discovered distance running on a frigid (19 degree) morning in Western Massachusetts. For the first time in my life I ran 13 miles on the Norwautuk Rail Trail. That run changed my life although it most certainly did not jump start any weight loss.
For 5 years I continued to go on 8 to 10-mile runs on weekends and shorter ones during the week. I've always been pretty active but the weight (190 to 200 lbs at 5'9") put me at borderline obese. The running or weight lifting never helped me lose weight until I discovered that it was all about sugar. Breads, pastas, chocolates, brownies all turn to sugar and get stored as body fat. Dairy and milk belong on a weekend pizza or morning coffee and nowhere else IMO.
No more WSD's (wheat, sugar, dairy) except on weekends and the weight is gone. I am at 166 pounds for the past year, still enjoy good juicy burgers with fries on the weekends, never drink sodas, eat my brownie once per week, and never feel hungry.
Some people have medical conditions but most of us just eat the wrong stuff (dining out more than a couple times per week will do anyone in - too much salt and who knows what in restaurant food). Losing 30 plus pounds helps me run easier, sleep better, work harder, and fit into sizes I wore in high school. All of us are a lot more responsible for our own lives than we think. Do it for yourself, your family, your community, and your job. Good luck.