Homophones that are not homographs are common in languages like English. This arises because several letters (or diphthongs) can have the same pronunciation. But where do the (less common) homographs that are not homophones come from? 'I shed a tear when I tear my clothes.' 'I read a magazine yesterday, today I read a book.'
Similarly to how you put it for homophones, we could say that sometimes, the same letter or digraph can have more than one pronunciation. "Ea" is actually a common example of this in English. The historical reasons for this are fairly complicated. Sometimes words with the same spelling but different pronunciations once had the same pronunciation (at least in some dialect) but developed differently for some reason. Sometimes they were never pronounced the same, but the spelling system doesn't mark the difference. Most spelling systems leave at least some information out: often stress or pitch, but sometimes things like vowel quality or length.
tear and tear
For tear and tear, it seems that the words ought to have developed the same vowel sound in at least some accents of English. The Oxford English Dictionary (OED) records "/tiːr/ /tɪə(r)/" as a dialectal variant pronunciation of the verb tear. The vowel in the verb comes from lengthening in Middle English of an originally short *e: this is expected to develop to Late Middle English [ɛː], which usually but not always turned into the "near" vowel when followed by the consonant /r/. The development to the "square" vowel instead is an irregularity that this word shares with some other words. This word is mentioned along with the other like examples bear, pear, swear, and wear in this handout about the Great Vowel Shift from Anthony Kroch's website.
The vowel in the noun tear has a more complicated etymology involving a lost fricative, but it is also supposed to have developed a pronunciation with [ɛː] in at least some dialects of Middle English. Here we see the regular development to the "near" vowel.
Kroch suggests that before /r/, the Middle English lengthening process might have resulted in a vowel that was subtly different from the already-long [ɛː] that was found in words like the noun tear. Another thing that seems relevant to me is that the verbs bear, swear, wear, tear all conjugate alike in Modern English (bore/born(e), swore/sworn, wore/worn, tore/torn); the past tense forms certainly show the influence of analogy and not just of regular sound changes, so it seems plausible to me that the vowel of the present tense for at least some of these verbs might also have developed through analogy.
read and read
The history of the forms of the verb read seems to be complicated, but it did have a long vowel in both the past and the present tense at some point. The long vowel ended up being shortened in the past tense, but not in the present tense. The OED suggests that the use of the spelling ea in the spelling of the past tense in modern English could be due to avoidance of homography with the adjective red.