1.She is tall for her age by two inches.
- She is taller for her age by two inches.
Which of the above two sentences is correct? If the two are correct, how?
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Both are unnatural. You can use "for her age" with the adjective tall,
She is tall for her age.
Or you can use "by two inches" with the comparitive form of the adjective (and with some reference for the comparison), taller,
She is taller than me by two inches.
But since one requires the standard form (tall) and the other requires the comparitive form (taller), you can't use both together.
If you need to be very specific about how much her height exceeds the norm, you can say something like
She is two inches taller than the average for her age.
She is two inches taller than the next tallest girl in her class.
She is in the 90th percentile for height at her age.
I would parse "she is tall for her age" as an idiom meaning something like "she is unusually tall among children of her age".
A comparable phrase which comes to mind is the White Stripes song lyric "you're pretty good looking (for a girl)". The implication is that within the set of girls, the person being described is among the more good looking.
Similarly, in "tall for her age", the implication is not a measurable comparison to an average / ideal child of the same age, it's a more general observation of her place within the set "children of her age". As such, the mention of "by two inches" doesn't mean anything, regardless of grammar.
As another comparison, consider "it was a hot day for the time of year"; it wouldn't mean anything to say "it was a hot day for the time of year by 10 degrees Celsius", because there is no base temperature to add 10 to.
As The Photon says, the sentence needs to be reconstructed to mention a specific height to compare to, such as "She's two inches taller than the average for her age".
In this case, we can eliminate the troublesome "by", like this:
She's two inches too tall for her age
Some people (likely non-native speakers) seem to find "by two inches" to be odd without some comparative phrase.
In fact "by two inches" doesn't require any superlative comparison any more than a sentence like "We are ahead by a century". The context of the sentence is sufficient to establish the comparison benchmark. For instance, in a conversation:
Q: How does her height compare to her age according to age-height average chart?
A: It looks like she's tall by two inches.
This is is perfectly fine, but of course, the second sentence is odd by itself, without the prior conversation. Even the first sentence is odd; it contains "her", which is a dangling pronoun without a prior discussion of some female person; we understand and accept that this is supposed to be an excerpt from a sensible dialog, and not the first words that two strangers exchanged upon meeting for the first time.
The phrase, "by two inches," implies comparison of items that are measurable in "inches."
In order for either phrase to make logical sense, one would have to know exactly how tall a female is, in inches, at any particular age.
Since humans exist in various heights, at various ages, the construct just isn't pleasing to the ear, nor understandable to know how tall she actually is.
The statement "She is two inches taller than most girls her age" would be more likely to be heard.
However, picture a room filled with other "girls her age." There would be a group of girls, of various heights, but then the girl in question would be a full two inches taller than the rest of the girls. This would NOT suggest "taller than average," but more "taller than the next tallest girl her age" with the tacit implication of reference to some finite grouping of females--maybe her soccer team, or perhaps, the math club.
Now picture a room filled with other "girls her age" of random heights evenly distributed from 5'4 to 5'8. Now let's say the girl in question is 5'8. She is certainly "two inches taller than the average" but glancing about the room, one's attention would not be obviously drawn to her for her height, as she may be only a quarter-inch taller than the next tallest girl. Quite unremarkable, and therefore would probably not merit mentioning.
So, ultimately, I would recommend settling with either:
if you agree with the preceding statements, or just