nor seeking glory from men (neither from you nor from others), when we might have claimed authority as apostles of Christ.
when we might have been burdensome: The word "burdensome" can have one of two meanings. It can refer to authority, in which case Paul is saying that he has not sought to throw his weight around, to pull rank on the new converts or to bring to bear upon them the weight of his apostolic authority. It can also refer to placing an unnecessary burden on someone. This is the likely meaning here. As the context shows, Paul does not wish to be financially dependent upon the Thessalonians. Such dependency would have been a burden on the brethren, suggesting that while some of them might have been rich, the congregation is largely made up of poor people. In the previous verse, the apostle repudiates covetousness, the desire for unlawful gain. Here, he says he also relinquishes a right and lawful claim to be supported by the Thessalonians (1 Corinthians 9:6-14).