I got certified when I was still quite overweight. But I was pretty fit aerobically too. If you think you are in good enough shape, go see a Diving Doc and get a professional opinion about whether you are fit enough to dive.
Also, while waiting for your back muscles to get used to carrying the gear (1) you may find it easier to put the BCD w/ its tank once you are already standing in the water and (2) don't put too much weight on a belt around your waist. Use the BCD weight pockets/trim pockets/tank weights or even a weight vest to get the weight up where it won't strain your back so badly. You need enough ditchable weight to make you bouyant but anything more than that can be secured where it feels most comfortable.
Also, while waiting for your back muscles to get used to carrying the gear (1) you may find it easier to put the BCD w/ its tank once you are already standing in the water and (2) don't put too much weight on a belt around your waist. Use the BCD weight pockets/trim pockets/tank weights or even a weight vest to get the weight up where it won't strain your back so badly. You need enough ditchable weight to make you bouyant but anything more than that can be secured where it feels most comfortable.