The First Continental Congress met in Philadelphia from September to late October 1774 in response to a series of acts passed in Parliament intended to punish the colonists of Massachusetts after the so-called "Boston Tea Party." Parliament designed these measures—known collectively in the colonies as the Coercive Acts and rebranded by American historians in the 19th century as the "Intolerable Acts"—to weaken the power of local government in Massachusetts and the economic power of the merchant class in Boston. Parliament knew that the Boston Tea Party was not popular among the colonial merchant class outside of Boston and did not, therefore, anticipate colonial-wide support. To their credit, in almost every colony there was some hesitation about the objectives of the First Continental Congress. The colony of Georgia did not send representatives.
To understand how the government in Nova Scotia reacted, it is important to recognize how Nova Scotia's colonial government differed from the government of many colonies to its south, and from New England's in particular. The crown established the Nova Scotia Council in 1720 and was comprised of only Governors, Lt. Governors, and appointed officials before 1758. Hoping to increase the number of settlers to Nova Scotia from Britain and New England, the Board of Trade pressured the Council to hold elections for a representative body. The first representative body met in 1758 and was comprised primarily of merchants from Halifax and close associates of Governor Charles Lawerence. Unlike the town meeting structure of New England that could exert influence (even if informal or extra-legal as was the case during the colonial crisis) over British officials and colonial politicians in the more urban ports, power in Nova Scotia largely flowed out from Halifax to the surrounding regions. During the 4th General Assembly, which sat from May 1765 to April 1770, much of the merchant class of Halifax actually raised grievances similar to those being raised in New England and throughout the colonies to the south. Stamp Act protests occurred in Halifax that resembled those in Boston, Newport, and New York. Colonists in Nova Scotia also celebrated the repeal of the Stamp Act in 1766.
But there was also a growing recognition among the Nova Scotia Assembly that the colony relied on Great Britain more so than their southern counterparts. The Lt. Governor estimated the yearly cost of maintaining good relations with the native people of region cost £400, on which they relied on British support. The colony also wanted for roads, which could only be built by soldiers and funds from Britain. There was hope that coal mining in Cape Breton would also grow thanks to the labor of soldiers. William Campbell, Governor of NS between 1766 and 1773 called British troops "the very life, soul, and support" of the colony.
By the time elections were held for the 5th General Assembly of Nova Scotia in 1770, questions about expanding the colony's infrastructure and increasing settlement outweighed questions of imperial politics and representation. The Assembly elected in 1770 sat for 14 years, meaning this group sat throughout the entire Revolutionary period. The sentiments of most (but not all!) of the Nova Scotia Assembly toward the colonists of Boston's protest to the Coercive Acts are perhaps summarized best by William Nesbitt, "The disorders in the colonies have arisen to the greatest height, and require coercive measures." Unlike in New England and beyond, the political elite in Nova Scotia had largely sided with Britain.
Many Nova Scotian colonists had colonial sympathies, especially the considerable number of "planters" who had come to the colony from New England during the 1760s. A shipment of hay bound for Boston to supply the British army was burned by suspected Nova Scotia rebels. News of the First Continental Congress reached Nova Scotia in early September 1774. But when rumors of support for this body reached Halifax, the troubled Governor and Assembly acted quickly to quell dissent. Governor Legge published a proclamation outlawing town meetings in the Nova Scotia Gazette on September 21, 1774.
So why didn't Nova Scotians rise up against this "abuse of power" and "destruction of liberty" like their cousins to the south? It is important to note another uniquely Nova Scotian issue that detracted from colonists' support for the First Continental Congress: the issue of a land tax that divided colonists and the government. As noted before, the majority of supporters for the nascent colonial cause had come to Nova Scotia in the 1750s and 60s from New England because of the opportunity for farmland that had been made available after the British government forcibly removed thousands of Acadians. Families were promised enough land to raise 30 to 50 heads of cattle without taxes for the first decade. But others resented the "New England Planters" for the generous offer they received. Matters were made worse when the Governor raised the tax on land owned by disbanded soldiers and not on the planters, many of who were still avoiding their taxes. To try and mend this division, the Assembly proposed a land tax that was based solely on acreage and would apply to all colonists. While the planters reluctantly agreed to the proposal, the soldiers who largely owned wilderness land were outraged as most their land was unprofitable. This question about land tax was, in many ways, directly connected to the issue of growth that dominated politics in the region. Had the colony been more self-sufficient, perhaps the pro-colonial movement would have gained traction. But as it stood, local issued trumped imperial ones.
There would be support in Nova Scotia after fighting broke out in April 1775 and for the Second Continental Congress. A group of pro-American colonists even met with Washington about an invasion of Nova Scotia and later fought a poorly-conceived attack on Fort Cumberland. But as before, the majority of the Nova Scotia government—and perhaps even common Nova Scotians—believed the colony needed support from Britain to continue to grow.
TL;DR: Not only was Nova Scotia's government structure much different than most colonies in what would become the United States, but Nova Scotians also depended on Britain more so than the colonies that would achieve independence.
Further reading:
Elizabeth Mancke, The Faultlines of Empire
Beamish Murdoch*, A History of Nova-Scotia, or, Acadie*
Neil MacKinnon: This Unfriendly Soil