There are a few places in the New Testament where Paul addresses the idea of the stronger brother and the weaker brother, usually in the context of the issue of eating meat which had formerly been sacrificed to idols (Romans 14; 1 Corinthians 8.4-13; 1 Corinthians 10.25-32).
It’s a fairly complex issue, but basically Paul says that since idols are nothing (because they represent gods which don’t actually exist), eating food which had previously been offered to them is no big deal. Stronger, more mature Christians would be able to realize this, and would see that eating such meat would not be inherently wrong.
However, weaker, newer Christians, especially those who had been recently converted from a pagan background, could struggle with the idea of eating meat which had been sacrificed to an idol, and could feel like they were compromising their faith by doing so. For these Christians it would be wrong for them to eat because doing so would violate their conscience.
Paul’s real focus in these passages is less on giving specific instructions on which activities should be partaken in and which should be abstained from, and more about teaching the stronger and weaker brothers how to interact with one another. Basically, they should treat one another with love: the stronger brother should be willing to give up meat forever in order to avoid leading his weaker brother to sin against his conscience, and the weaker brother shouldn’t try to bind his stronger brother’s actions by his own conscience.
In many ways, Paul’s thoughts are summed up in Romans 14.3:
“Let not the one who eats despise the one who abstains, and let not the one who abstains pass judgment on the one who eats, for God has welcomed him.”
Depending on the issue, I think I have been both the weaker and stronger brother at different times, and what Paul commands in Romans 14.3 is challenging to both groups.
The stronger brother is not to despise the weaker. I’ve seen this happen a lot, and it can be tempting to do. We grow frustrated at the qualms of our weaker brethren and so it gets easy to ridicule them as hopelessly backward and just write them off completely. Maybe make jokes about their limited understanding and speak with condescension to and about them.
The weaker brother is not to pass judgment on the stronger. This is tempting as well. Since our brothers are doing something that our own consciences won’t permit us to do, we are tempted to view them as less holy or less devoted to their faith than we are. Perhaps we even cease to think of them as faithful Christians.
As Paul points out in the verse above, both of these attitudes are wrong. Regardless of which side we find ourselves on, we have to be careful about how we treat each other: love and respect for our brethren should always be our primary response.