Both the English and metric systems, as popularly understood in the early 19th century, had a unit of ‘weight’ (to use the English word), a term used (then and sometimes now, as on this cereal package in front of me) indiscriminately for either mass or force of gravity; the difference between these was only newly appreciated by physicists.
As the systems matured in scientific usage, they sprouted units of both mass and force, perhaps too many rather than two few!
In the metric system, the gramme(g) is the basic unit of mass, although many derived units are based on the kilogramme (kg, 1000 g). One unit of force is the dyne (dyn, the amount of force necessary to accelerate 1 g by 1 cm/s over the course of a second); another is the newton (N, the amount … 1 kg by 1 m/s …). For what it's worth, the newton is the official unit in the International System of Weights and Measures, but not everyone pays attention to that, even where they use the metric system, any more than Americans pay attention to the metric system.
In the English system, things are even more complicated, because ‘pound’ is used for both a unit of mass (lbm) *and* a unit of force (lbf). So, the poundal (pdl, the amount … 1 lbm by 1 ft/s …) is the unit of force to go with the pound mass, while the slug (the amount of mass that 1 lbf can accelerate by 1 ft/s over the course of a second) is the unit of mass to go with the pound force.
Actually, the metric possibilities are just as great (or greater, since, as above, people don't always agree on whether to use the g or kg and the cm or m), although the others are less common. To this day, the Chinese space programme uses the gramme force (as called the pond), or so Wikipedia tells me. The unit of force to go with that is the hyl (the amount of mass … 1 pond … 1 m/s …).
So you see, both systems have all the units you could want —and more!