I don't know if this is what you do, but I've definitely noticed that working seriously on the power lifts (squat, deadlift, overhead press, bench press) has made my joints feel better throughout the day.
It does nothing, except maybe bad things, if you don't know the cause of the back issues.
all people should stay away from heavy deadlifts until they have mastered good form of course.
As an aside, GPs tend to give bad advice on all matters of sports medicine.
So yep, I'm convinced lifting heavy stuff is good for your back (IF you use good form, of course.)
Studies like this have shown that herniated discs and other types of damage once thought to be the cause of back pain are present in pain-free people with a high rate of incidence.
Further, it's not known what the tradeoffs are in terms of risking damage vs the benefits of increased strength.
I do think extra research is needed.
FWIW your definition of heavy and mine seem to be about the same: A weight the subject can lift with perfect form for a small number of reps, e.g. <= 5. With training, likely to be in the range of bodyweight x 2 and up.
It would be strange if having the strength to lift twice your bodyweight or more would somehow be necessary for a healthy back. There are safer ways of increasing strength of the weakened muscles, but first it would be good to identify whether indeed weakened muscles are the cause of one of the causes of your problem. That's all I am saying - deadlifting is not in general a safe recommendation for undiagnosed people with back issues.
Source: my GP when he told me I was basically fat. :)