Thanks a lot is the ordinary use in conversation, or bare thanks! Many thanks is more frequent in writing, particularly in formal writing. Thanks much is unusual.
Here's a Google NGram. Keep in mind that the underlying corpus here is printed works, so the more formal phrase is significantly overrepresented.
For a learner of English as a second language, mastering all the subtleties of the present continuous or progressive tense is probably the hardest to achieve but among the the most communicative aspects of English.
This particular case I find too overwhelming to try to de-construct, but will an example do? If my daughter returned home from her new boarding-school and said,
"I don't really like it very much over there."
I'd ask her what was wrong, perhaps encourage her to give it more time. Whereas if she said,
"I am not really liking it very much over there,"
Then I might ask if she'd rather come home for good. If I give you a clue as to why, it's partly only subjective:
Grammatically, you use a "..ing" word for things you do actively, like
"I am watching TV" or "I am listening to music".
Whereas verbs for things you cannot help doing do not tend to end in "..ing"
"I see the sky" or "I hear music." "I like it here"
Now, when you deliberately add an "..ing" to something you cannot help, well..personally, in my daughter's case, it would give me the impression she'd been *trying to like it" in her new school, but hadn't succeeded - yet was still trying.
FWIW
Best Answer
All of these sentences are grammatically correct, but you won't hear the last one very often, and probably never* encounter the first one. They mean different things.
These are possible ways of referring to how often someone feels sleepy. That is, how frequently. There is some of the statement left off, which would make these sentences:
When someone says “too” they are suggesting an excess beyond an acceptable level. In this case, the acceptable level would be feeling sleepy at regular times or just at the end of the day. The following dialog is possible:
“Too” is also used in one of your other examples:
Again, someone saying this is implying a tolerance limit that has been exceeded. Someone might make this declaration as they left the company of a group late at night, and the implication would be that they are too sleepy to continue doing what they are doing. More likely you’d hear it in situations like this:
Most people would say that they are sleepy (not that they “feel” sleepy) unless they are describing something that is similar to sleepiness, especially something externally imposed. c.f.:
More likely people who are very sleepy in normal situations will just say “I am very sleepy.”
1 ☼ = descriptively ungrammatical (violates practice, but not rules).