Relative frequencies of words of a certain length?

That data sounds a bit specialised, so I'm not too surprised you can't find it. It would be very dependent on the type of text you take as input. There is lots of data on relative occurrence of particular words or number of times words appear in text.

The is the nearest I could find:

                          blogs    news twitter

avg.word.length            4.0     4.3     3.7

Analysis of text data and Natural Language Processing: Coursera’s Data Science Capstone Project

Their description of how that and other data was generated might give you a start in generating the statistics yourself (if you have any programming skills - otherwise persuading someone else to help you!)

If you can't access a suitable corpus of text to use, Project Gutenberg might be a good source.

Do you mean words that are frequently used, or words in a dictionary? I assessed the word lengths from two dictionary lists I have, with these results:

Length  Words   Words
1       2       2
2       51      128
3       580     1182
4       2655    4736
5       5098    9739
6       7959    17879
7       10222   25282
8       10778   31855
9       10049   32020
10      8475    30590
11      6230    25859
12      4354    20391
13      2849    14877
14      1702    9744
15      670     5919
16      470     3373
17      260     1811
18      119     838
19      50      429
20      14      332
21      1       0
22      1       0
23      1       0
Total   72590   236986
Average 8.6     9.6

But this does not represent common usage. Words tend to evolve into smaller words due to frequent use.

For example boatswain to bosun.