What was a Battalion?
(1) A command made up of two or more companies whose members were often detached for special duties as pioneers, sappers or sharpshooters.
(2) Companies of Infantry temporarily serving apart from a parent body; commanded by a Lt.Col. or Major; included a Headquarters company & several artillery batteries.

What was Artillery?
Soldiers trained, armed, and equipped to use large-caliber guns, mortars, and howitzers.

What was a Infantry?
Soldiers trained, armed, and equipped to fight on foot. The word is derived from the European reference to foot soldiers who had in their youth formerly been servants and followers of knights.

What was a Cavalry?
Soldiers trained, armed, and equipped to fight on horseback. The branch was distinguished from dragoons (horse soldiers trained to fight on foot or in the saddle) and mounted infantry (which was trained to fight on foot.)

Cavalry soldiers did have to provide their own horses (usually two or three).
Don't know about the weight.

They would "volunteeer" for whatever branch of service they wanted but if the joined the cavalry and lost their mount(s), they were usually reassigned to the infantry.