Needless to say, the Bible is quite permissive about what we can do. There are very few restrictions on food, drink, festivals, music, clothing, and all sorts of other things. It could even be argued, though I would prefer not to, that smoking is entirely permissible.
But with that liberty comes responsibility. Though "all things are lawful", we are warned that not all things are beneficial. I like the way Mike Winger looks at this. The stronger brethren may well have the stronger faith, however they also have the higher tendency to fall towards licentiousness. If you believe, for example, you have the right to drink alcohol, you are far more likely to get drunk than a teetotaller. They're not going to get drunk because even if alcohol is not necessarily wrong, they don't touch the stuff, and so will not take their liberty to the excess.
Obviously, all human beings are flawed. We sin, whether we're strong enough to embrace the liberty afforded to us by Christ, or weak enough to not believe in it. Stronger brethren may become licentious, weaker brethren may become proud, but ultimately, the Bible has this one message for us both: Grow up. We are called to unite under Christ, edify each other, and do what is best for each other. This never ending conflict of personal opinions should exist to keep us in check, not blow the Church apart like some heretical cult.
Therefore, let us stop with the petty squabbles, respecting each other, and not judging each other, for that is God's job. That which Scripture condemns, let us all condemn with one accord. That which Scripture promotes, let us promote with one voice. That which Scripture neither condemns nor approves, let each be fully convinced in their own mind, and not seek to restrict or impose upon each other.