Is TV a common or proper noun? If it is common, why is it capitalized?
It is common because TV is actually an abbreviation of television, which is an object, therefore it is a common noun. It is capitalized because it is also an acronym.
TV is a common noun, an acronym for the common noun television.
It's customary to use capital letters for acronyms even when they're common nouns.
Some acronyms are common nouns and some are proper nouns. The only way to tell is to know what the acronym stands for, such as:
AC = air conditioning, a common noun;
ASAP = as soon as possible, a noun phrase;
IQ = intelligence quotient, a common noun;
UFO = unidentified flying object, a common noun;
FBI = Federal Bureau of Investigation, a proper noun;
UN = United Nations, a proper noun;
NAPOLCOM = The National Police Commission (Philippines), a proper noun.
Abbreviations can also be a shortened form of a common noun or a proper noun, such as:
abbr. = abbreviation, a common noun;
lb. = pound, a common noun;
hr. = hour, a common noun;
mg. = milligrams, a common noun;
no. = number, a common noun;
Inc. = Incorporated, a proper noun as part of a company name;
Jan. = January, a proper noun as the name of a specific month;
Lt. = Lieutenant, a proper noun as the title of a person.
Then there's the whole world of abbreviations and acronyms used in texting. The only way to know if it's a common noun or a proper noun is to know what they stand for and to know the difference between a common noun and a proper noun.