I calculated the entropy for "variable", "property" and their concatenation "variableproperty" (with e.g. the Shannon Entropy) and got $2.75, 2.5$ and $3.33$ respectively. These are all entropy per byte, if I don't err. But why is the last value greater than the other two and not lying between them?
The calculator you've linked to is calculating the Shannon entropy of the character frequency distribution of your text. That is, if you type in e.g.
variable, what it will calculate is the entropy of the following probability distribution:
p("a") = 2/8 = 0.25 p("b") = p("e") = p("i") = p("l") = p("r") = p("v") = 1/8 = 0.125
In particular, you would get the exact same result if you typed in
aabeilrv or any other permutation of the letters in the word
variable. Repeating the input several times won't change the letter frequencies, and thus their entropy, either.
Essentially, the entropy value returned by that calculator may be considered a measure of how many questions it would take, on average, to correctly guess a letter picked at random from the input text, using yes/no questions like "is the letter a vowel?" or "is it before N in the alphabet?", assuming that we know the text it has been picked from.
Based on this, it should be obvious why the input
variableproperty gives a higher entropy value than just
property alone: the combined input string has more distinct letters, and thus it's harder to guess which letter a randomly chosen one of them might be.