IOTL, Thomas Jefferson (then the Secretary of State) recommended that the United States adopt a form of the metric system in 1790, in his so-called "Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States". This would have had considerable similarities to the metric system of OTL, except for using somewhat different bases for the units (e.g., the length of a second pendulum as the basic length measure instead of the length of a meridian) and, more significantly, adopting existing terms rather than a system of prefixes for different units. For example, the foot was to be the basic unit of length, somewhat shorter than OTL's foot, but a mile would then be exactly 10 000 feet (just shy of 3 km IOTL's units, or 1.85 of our miles).
This proposal was taken up by Congress several times given their constitutional authority to regulate coinage, weights, and measures, but while it occasionally made some progress and even passed the House, it never cleared the Senate and ended up being abandoned once surveying of the Old Northwest started using the old units. The problem seems to have been a combination of opposition from certain existing interests who weren't very interested in changing units and the decision by the French to adopt a wholly separate metric system in 1792, which undermined some of the justification of Jefferson's system (which was intended to harmonize with metrication ideas that were current in 1790).
But either of these could easily enough be overcome. The idea did also have significant proponents--Jefferson himself, of course, but also Alexander Hamilton (and it's rare you see Jefferson and Hamilton on the same side!), James Madison, James Monroe, and George Washington--so even a slight weakening of the opposition through one or another being ill or dying or simply having different committee assignments could easily tip the balance and get it through the Senate. And it was hardly preordained that the French would adopt precisely the system that they did. One could easily enough imagine them sticking to the original, Jefferson-like proposals, making Jefferson's proposal itself look more attractive as a means of harmonizing U.S. measures with the French and adopting a rationally designed international system, or simply taking longer to metricate so that the U.S. isn't discouraged by the French breaking with the Jefferson-type system.
So, what would the effect on the United States be if it rejected customary English units in the 1790s, at least formally, and adopted a kind of metric system? Certainly in the short run I doubt it would have much effect outside of the United States, except that possibly the French might have a metric system more similar to Jefferson's proposal. In the longer run, though, it might be easier to harmonize U.S. units with the rest of the world, and there could be some interesting effects on trade and importing technology, e.g. it might be easier for the U.S. to trade with metric countries and harder to trade with other countries, especially in terms of adapting foreign technology. Perhaps this could end up having significant effects down the line.
This proposal was taken up by Congress several times given their constitutional authority to regulate coinage, weights, and measures, but while it occasionally made some progress and even passed the House, it never cleared the Senate and ended up being abandoned once surveying of the Old Northwest started using the old units. The problem seems to have been a combination of opposition from certain existing interests who weren't very interested in changing units and the decision by the French to adopt a wholly separate metric system in 1792, which undermined some of the justification of Jefferson's system (which was intended to harmonize with metrication ideas that were current in 1790).
But either of these could easily enough be overcome. The idea did also have significant proponents--Jefferson himself, of course, but also Alexander Hamilton (and it's rare you see Jefferson and Hamilton on the same side!), James Madison, James Monroe, and George Washington--so even a slight weakening of the opposition through one or another being ill or dying or simply having different committee assignments could easily tip the balance and get it through the Senate. And it was hardly preordained that the French would adopt precisely the system that they did. One could easily enough imagine them sticking to the original, Jefferson-like proposals, making Jefferson's proposal itself look more attractive as a means of harmonizing U.S. measures with the French and adopting a rationally designed international system, or simply taking longer to metricate so that the U.S. isn't discouraged by the French breaking with the Jefferson-type system.
So, what would the effect on the United States be if it rejected customary English units in the 1790s, at least formally, and adopted a kind of metric system? Certainly in the short run I doubt it would have much effect outside of the United States, except that possibly the French might have a metric system more similar to Jefferson's proposal. In the longer run, though, it might be easier to harmonize U.S. units with the rest of the world, and there could be some interesting effects on trade and importing technology, e.g. it might be easier for the U.S. to trade with metric countries and harder to trade with other countries, especially in terms of adapting foreign technology. Perhaps this could end up having significant effects down the line.