The emphasis is on one another's, in contrast with the selfishness which leaves others to take care of themselves. The primary reference in burdens is to moral infirmities and errors, and the sorrow and shame and remorse which they awaken in the offender.
So (οὗτως)
By observing this injunction.
Fulfill (ἀναπληρώσατε)
The verb denotes, not the filling up of a perfect vacancy, as the simple πληροῦν, but the supplying of what is lacking to fulness; the filling up of a partial void. Comp. 1Co 16:17; Phi 2:30; 1Th 2:16.