Is the following sentence grammatically correct?
I bought a real heavy book.
I feel it should have been a really heavy, but I heard people use a real heavy all the time.
Is the following sentence grammatically correct?
I bought a real heavy book.
I feel it should have been a really heavy, but I heard people use a real heavy all the time.
It is common in speech, not so much in writing. The same could be said, more or less, for any shortened form of -ly adverbs.
As for using "real" or "really" to mean very or quite, well—opinions vary on the advisability of this usage in formal writing. But I would not advise using it in your Masters thesis, for example.
Grammatically, it is perfectly correct and standard. It's of the form:
[Noun/pronoun] [verb] [article] [adverb] [adjective] [noun].
Where the adjective modifies the following noun, and the adverb modifies that adjective.
The question isn't one of grammar, but whether real can be used as an adverb.
Real has been used this way since the mid-17th century at least, but only in some regions. This has led to it generally being considered of colloquial or informal use. In such uses it is arguably superior to really as using real may seem more genuine and less fussy, but in formal use really would be preferred by the same token.
It is probably grammatically okay, but would be considered immature and poor quality writing unless spoken as dialog by a particular type of character. One should also avoid words like "very". Instead choose words that are strong without modifiers. In this case "onerous" might be a good choice. Others: weighty, burdensome, depending upon the shade of meaning one is seeking .
Source is "Strunk and White" and "Roget's Thesaurus".