There were a few guys on sister platoons and my platoon that lost a substantial amount of body weight, in the realm of 40lb+ on basic. A few of them kept it off, others gained it back on. It depends on whether you are diligent (i.e. don't hurt yourself and end up on a TCAT for 6 months) and are self motivated. One guy that managed to keep it off had terrible knees and compartment syndrome but managed to stay fit with low impact activities like biking and swimming, he ended up reducing his body weight by half in less than a year. On the opposite end of the spectrum was a guy that started eating large pizzas as snacks, demolishing entire boxes of powdered donuts while he played video games at night and increased his BW by 30+%.
People tend to lose some weight on basic, just due to the sheer physical demand but most go back to their normal, "pre-basic" weight in no time if they are moderately fit.
Generally, instructors and supevisors are appreciative of anyone giving their all doing PT, even if they aren't the fittest person in the world.