Romans 14 begins with the imperative, “accept the one who is weak in faith” [NASB]. The first thing to notice is who this command is given to. This command is given to those who have authority to decide who is accepted into the church and who is not, i.e., the leaders of the church. Paul is telling the church leadership to accept the one who is weak in faith into church fellowship. This tells us something else about those who the command is given to: they are not weak in faith. Notice, also, that there is no command addressed to the weak in faith to accept the one who is not weak in faith.
Paul’s instruction in Romans 14 assumes that church leaders are not weak in faith and that those who ARE weak in faith will not be in positions of church leadership. I think this conclusion is strengthened by Paul’s admonition to those who are not weak in faith to refrain from activities that might harm someone who is weak in faith. The weak in faith are never given a complementary admonition. The weak in faith are to be protected, taken care of, etc.
In my opinion, whatever weak in faith means, those who are in that category should not be in positions of church leadership.