There's a long history of "light infantry".

The distinction began when body armour and discipline were introduced (especially in Greece and its cultural influence zone, including Italy).
Skirmishers were quite important in the last generations before Alexander the Great. They were elusive enough to avoid decisive close combat (few horsemen in Greece) and armed with ranged weapons (slings, javelins or bows). Such skirmishers were quite quick on their feet and thus also useful for foraging, attacking enemies on mountain peaks and pursuit.

The idea of "light" infantry has other strong examples in the 18th century; less-disciplined Austro-Hungarian border militia infantry ("Grenzer") and German Jäger ("hunters") skirmishers. The standard line infantry weapons of the time were terribly inaccurate muzzle-loaded smoothbore muskets. Muzzle-loaded rifles were slower firing (unable to stop infantry charges), expensive and required more skills.
Units with recruits of forester descent were raised and equipped with rifles in order to produce skirmishers and because they (due to an elite status and privileges) did not desert as easily as normal line infantry. Army leaders avoided to march line infantry through forest areas, sending them to forage or on picket duty because they deserted too easily (much of Germany is mostly covered by forests, though!).

Technology changed and line infantry got breech-loaded rifles that fires accurate and quick. The line infantry also got more loyal thanks to nationalism and became able to do what light infantry was able to do before.
Light infantry morphed (with breaks) to "sharpshooters" and "snipers".

It's similar with the Stoßtruppen and Arditi of WWI; innovative at their time (and nowadays labelled as "light infantry", especially the Stoßtruppen), but their advantages were either obsolete or incorporated into line infantry till mid-WW2.


To sum it up; "light" infantry was post-Renaissance pretty much the vanguard in infantry development. The line infantry absorbed light infantry traits over time (without really being "lightweight").