What does "толка" mean?
I know that 'но толка немного' = 'But only a little', so here I assumed it meant something like 'only,'but what does it mean in the context of this song lyric:

"Песня музыканта, Санта Лючия
Смотри в глаза мои, но только-только не лечи меня
Острый, как чили, я сладкий, как мёд пчелиный"

And why is it repeated? Just for rhythm? (It is a rap portion so that would make sense)

Question

What does "толка" mean?
I know that 'но толка немного' = 'But only a little', so here I assumed it meant something like 'only,'but what does it mean in the context of this song lyric:

"Песня музыканта, Санта Лючия
Смотри в глаза мои, но только-только не лечи меня
Острый, как чили, я сладкий, как мёд пчелиный"

And why is it repeated? Just for rhythm? (It is a rap portion so that would make sense)

Answer

толк - sense. 
но толка немного - no much sense.
от него нет толка - he is useless

только - just only, 
только-только не лечи меня - don't, don't "cure" me (don't make me feel I am wrong)

толк and только are different words.

Answer

Толка мало , без толку , а что толку ? , без всякого толка - it is mostly then there is no sense from something , somebody . 
Безтолковый -adjective - the same as stupid

Answer

First sentence: "но толка(толку) немного" means "but little of use" and word "толк" implies "use" here.

Second sentence:
"Смотри в глаза мои, но только-только не лечи меня"
Look at my eyes, but only-only don't press me/don't press my buttons"
something like this...

There is two different words with two different meanings: "толк" and "только"...

Answer

I know I spelled it wrong, I can't get my keyboard to cooperate with cyrillic