Why did others support the Jamestown settlers?
For the first decade and a half of its existence, the English settlement at Jamestown received support from the Virginia Company, a joint stock company composed of London investors that founded the colony under a royal charter. The company supported the colony (albeit a bit inconsistently) out of the hope that they could derive a profit from the colony if it could survive. To this end, they sent supplies and especially additional colonists, including large shipments of indentured servants and craftsmen from England and the continent. Their motive in doing so, again, was from profit, though their expected source of profit changed when, after failing to locate sufficient mineral wealth, the colony turned to other pursuits, culminating with tobacco cultivation. This required a large influx of capital, both in the form of human labor and wealth, and it took the lobbying of Virginia Company leaders such as Sir Thomas Smythe in England and John Smith and John Rolfe in Jamestown itself to sustain support for the project.
After open conflict with the area Indian peoples (some of whom had also initially supported the colony in the hopes of strategic advantage) the colony came under the direct control of the Crown, which annulled the charter of the Virginia Company, which was losing money on the venture in any case. James I and his successors continued to support Jamestown both in the hopes of creating a profitable colony and out of strategic considerations. They hoped to establish a foothold on the continent (New England was still in its infancy at the time) as a check on French and especially Spanish expansion. In sum, it was out of the hope for profit and strategic advantage that the Virginia Company and the Crown supported the endeavor at Jamestown.