Also remember that there are 2 types of dependance: psychological and physiological.
All drugs have a psychological dependance. They make you feel good, hence you want to have more. But some-- example heroin and other true narcotics-- also have a physiological dependance that comes along at a variable time afterward. Variable, because it is usually dependant on doing a certain amount over a certain time period, for your body to "adapt" to it...
Though one may say that psychological is only a biochemical hence also physiological of mind addiction-- pure physiological, has to do with your system developping tolerance and then physical withdrawl symptoms once deprived. It is these unpleasant withdrawl symptoms which make you want to return to the non deprived state, hence crave the drug. For example, the nausea, vomiting, diarrhea, shivers, stomach aches of heroin withdrawl are purely physiological. Some drugs like cocaine have a much stronger -if not exclusively psychological according to some reasearchers-- psychological addictive power.
So explaining drug addiction by "weakness of the mind" is inappropriate. You can say weakness is having succumbed to try it... or to re-do it... But this is plain wrong. It does take a good dose of willpower to resist certain temptations... But addiction-prone personalities have been recognized for years and they have nothing to do with the "classical" strong vs weak minded personalities. It has much more to do with thrill seaking personalities. For example, someone who does extreme sports (sky diving, bungee, deep diving, free climbing... ) is much more at risk of getting addicted to multiple things than people who like a comfy grand-pa no waves type of life...