ok a few points trashman308.
1. the definition of obese can differ alot it can range from being considered "overweight" upto "grossly overweight"
2. 4km isn't really all that far
3. how strong is strong. if you have a substantial amount of muscle mass, that can put out your bmi.
4. I'm in a similar situation to you i'm about 184cm and 100kg, I play youth league basketball and have 2 hour training sessions twice a week plus i have atleast 3 games a week, I also play soccer, cricket and tennis around this. I am probably fitter and faster than alot of people within the optimum range of the bmi and I'm also quite strong that doesn't change the fact i'm still overweight... the bottom line is that if it bothers you just loose the weight.
5. Unless your weight is impacting upon your health etc. its more about whether or not your happy with your current shape.
As far as weight loss is concerned really its what works for you. I'm grabbing myself a gym membership in the next couple weeks. I'll probably try fit in around an hour workout on week days of which ill probably spend 1/2 hour on a treadmill or bike and half an hour on weights, there is nothing wrong with doing weights if you play football it'll probably assist your game performance anyway but you'll probably want to mix it up with some cardio based stuff anyway... plus that way it would be more beneficial for weight loss purposes.
As most people have said diet plays and important part no need to go overboard just make sure your eating good food at normal meal times, which in my case basically meant 'don't be eating toasted cheese sandwhiches at midnight'.
basically if you want it bad enough you'll do it but dont be doing it just for the sake of conforming to the BMI.