"I feel bad for you" versus "I feel badly for you"

What is the correct usage? Apparently it is "I feel badly", but but wouldn't that mean you have an inadequate ability to feel?

Assuming you're talking about a situation where something bad has happened to your friend, and you're saying you feel unhappy on their behalf, then "I feel bad for you" is correct.

You are right that "I feel badly" would mean you are having difficulty in feeling at all - which would be a rather unusual thing to say :)

In general the verb "to feel" will take an adjective (happy, sad, good, bad, angry, relieved) after it to indicate the feeling, rather than an adverb.

Certain verbs like feel, smell, and taste take adjectives as complements, not adverbs. If you use an adverb with them, it changes the sense altogether, because it now modifies the verb rather than serving as a predicate complement describing the subject.

• Sour milk tastes bad. Honey tastes good.
• I feel bad that I didn’t go. I feel good about that.
• Those flowers smell good. That sewer smells bad.

Contast with:

• He tastes poorly because he’s burnt his tongue.
• My fingers feel badly when I have gloves on.
• A man with no nose smells poorly if at all.

So you can have a dog that smells bad but like all dogs, he nonetheless smells well.

"I feel badly for you" sounds like teen-speak for "I am attracted to you". You probably meant "I feel bad for you".

You cannot use badly as a verb. It will always be an adverb. In those two sentences, feel is your verb, which links an adjective (in this case bad) to the subject. Badly would be used to describe how something was done.

I feel bad for her.

She was hurt badly.