As discussed under Jacob 2:23, the earliest Book of Mormon text had three occurrences of the archaic burthen. These have all been edited to burden in the LDS text but not in the RLDS text. Here in Mosiah 6:7 the change from burthensome to burdensome was first made in the 1906 largeprint edition and then in the third printing (in 1907) of the 1905 missionary edition and the 1907 vest-pocket edition. The critical text will, of course, restore the archaic burthen wherever it is supported by the earliest textual sources.
Summary: Maintain in Mosiah 6:7 the archaic form burthen (“that thereby he might not become burthensome to his people”).