Notes from Matthew 17:17-20
The disciples had been unable to cast out this demon, and they asked Jesus why. He said their faith was too small. It is the power of God, plus our faith, that moves mountains. The mustard seed was the smallest particle imaginable. Jesus said that even faith as small or undeveloped as a mustard seed would have been sufficient. Perhaps the disciples had tried to cast out the demon with their own ability rather than God's. There is great potential in even a little faith when we trust in God's power to act. If we feel weak or powerless as Christians, we should examine our faith, making sure we are trusting God's power, not our own ability to produce results.
Notes from Luke 17:6
A mustard seed is small, but it is alive and growing. Almost invisible at first, the seed will begin to spread, first under the ground and then visibly. Like a tiny seed, a small amount of genuine faith in God will take root and grow. Although each change will be gradual and imperceptible, soon this faith will have produced major results that will uproot and destroy competing loyalties. We don't need more faith; a tiny seed of faith is enough if it is alive and growing.
Notes from Romans 14:1ff
What is weak faith? Paul is speaking about immature faith that has not yet developed the muscle it needs to stand against external pressures. For example, if a person who once worshiped idols became a Christian, he might understand perfectly well that Christ saved him through faith and that idols have no real power. Still, because of his past associations, he might be badly shaken if he unknowingly ate meat that had been used in idol worship. If a person who once worshiped God on the required Jewish holy days became a Christian, he might well know that Christ saved him through faith, not through his keeping of the law. Still, when the festival days came, he might feel empty and unfaithful if he didn't dedicate those days to God.
Paul responds to both weak brothers in love. Both are acting according to their consciences, but their honest convictions do not need to be made into rules for the church. Certainly some issues are central to the faith and worth fighting for, but many are based on individual differences and should not be legislated. Our principle should be: In essentials, unity; in nonessentials, liberty; in everything, love.