In order to re-route and build a line and new bridge upriver from the Sibley section, a very expensive new bridge would need to be built over the river, and significant structures would also need built over north-of-the-river wetlands in order to rejoin the existing mainline in Levasy. The necessary right-of-ways and environmental hurdles to do this make this option unlikely at best.
It would be possible to either rebuild the existing bridge to double-track, or erect a parallel bridge, as there is room for the extra track on the bluff and fill at either end of the existing bridge. Either of these would be very expensive as the bridge is long and massive, as stated by the previous poster.
Since the single-track section is short, the delays for the rail traffic are infrequent. It is rare for a train to wait on either side for more than five minutes, and the majority of traffic is spaced to allow for no delays whatsoever. Based on that (no real need), it will remain single track for the forseeable future.