My love = my affection for you. However, it could mean 'you, the beloved, you, whom I love', and could include a suggestion of deterioration in the appearance of the youth. The words seeming, and show are echoes of the concluding line of the previous sonnet. They usally carry overtones of hypocrisy and false covering for something which is not all well within. Here however the opposite is the case, or so the poet declares, in that his love shows itself as weak, and seems to be less than before, but in reality it has become stronger. Whether one believes this declaration or not is perhaps not relevant. Within the conventions of sonneteering the lover's words are gospel and the beloved is faultless. But the mere fact that the protestations occur as justifications for a period of silence, and that they are set in a group of sonnets which follow on from some in which abandonment, (87-9), hatred (90), deception (94-6) and separation (97-8) are the themes, leads one to suspect that the protestations themselves are mere show, a failing or tired love which is covered over with elegant and skillful wordplay.

See the note above. The poet claims that the ostentatious show of his love, which in former times was evidenced by frequent sonnets (and other declarations?), he now considers to be superfluous, and he does not wish to cheapen his love by making it too public and shallow.

That love = any love (which is advertised, publicised, put up for sale by the owner);
is merchandized = is made into a commodity, is reduced to the level of an object of trade (or prostitution).
whose rich esteeming = the precious worth of which.

3-4: 'Any love, when its preciousness is broadcast to the world as if it were a piece of merchandise, has its value reduced to that of a mere commodity on the market place'.

publish = make public, broadcast, make known to the world. There is a strong suggestion in these two lines (3-4) of pimping and prostitution. Compare for example the prostitution scene in Pericles, where Marina's qualities are trumpeted to the world:

[Exit]
.............................

[Re-enter Boult]

Springtime and love were proverbial companions. Cf. the song in As You Like It:
It was a lover and his lass,
With a hey, and a ho, and a hey nonino,
That o'er the green corn-field did pass
In the spring time, the only pretty ring time,
When birds do sing, hey ding a ding, ding:
Sweet lovers love the spring. AYL.V.3.14-19.

It is not implied that the poet first became acquainted with the youth in the springtime.

I was wont = I was in the habit of, I was accustomed to.
greet it = welcome it, celebrate it, salute it.
lays = songs, poems. See the notes on the following:
Yet nor the lays of birds 98.5

Sing to the ear that doth thy lays esteem 100.7

Philomel - the classical name for the nightingale, which apparently sings in early summer. Shakespeare uses it here, as also in MND.II.2.13-14, Philomel with melody, Sing in our sweet lullaby, without any obvious reference to the rather brutal story from the classics, given in Ovid's Metamorphoses VI.424-674. Philomela was turned into a nightingale after taking revenge on her brother in law, Tereus, for being raped by him. Procne, her sister, became a swallow, and Tereus a hoopoe.
summer's front = the beginning of the summer, early summer.
front also meant forehead. Compare this from Coriolanus:

one that converses more with the buttock of the night than with the forehead of the morning: COR.II.1.

The nightingale sings most in early summer, when seeking a mate.
The tunes of the nightingale are stale in the middle of summer, because we hear them at the coming in of the spring.
The Great Frost of Jan 1608. Reprinted in E. Arber, An English Garner, 1877, Vol 1, p.88.

stops his pipe = ceases to sing. The pipe was the traditional shepherd's instrument, so any music of the countryside could be referred to in such terms, since the natural music of the fields was regarded as the source of all melodies. We tend to underestimate how close the Elizabethan age was to all the sounds of nature. Even in London, which was then a large city, fields and gardens were always close by. Roads were not tarmacked and concrete was almost unknown. (OED.3.a. gives the earliest use of the word concrete in this sense as 1834, although concrete of some sort was in fact used by the Romans). One would not have to leave the city to hear a nightingale sing. For us such sounds are obscured, masked and obliterated by city living. See for example Bottom's speech in Midsummer Nights Dream:
BOT. I will walk up and down here, and I will sing, that they shall hear I am not afraid.
[Sings]
The ousel cock so black of hue,
With orange-tawny bill,
The throstle with his note so true,
The wren with little quill,— etc. MND.III.1.113-7

Bottom automatically finds his security in the rural memory of birds and bird song.

his - editors often emend this to her, in conformity with lines 10 & 13. Arguments in favour of retaining his are given by GBE p.211, and JK p.306. (among others).
riper days = days of ripeness and plenty, as the summer advances into autumn.

Not that = it is not because etc. I.e. I have not ceased writing sonnets to you because the summer of our love is less pleasurable than the springtime was, when the nightingale etc..

her - through the influence of the legend the singing nightingale was thought of as female. It may not have been known at the time that it was the male which was the chief songster.
mournful hymns - sad tunes, (because of Philomela's tragic story). Bird song at night however would be considered mournful, in harmony with the darkness of night.
hush the night - the night appeared to become hushed as if listening to the song of the nightingale. This is a frequent experience, even today, of those who actually do listen to a nightingale singing.

But that = but because.
wild = savage, uncultured. In contrast to the measured chants of the nightingale the undisciplined songs of other birds were wild and savage. Note however that wild and vile (vild) were interchangeable words of unfixed spelling (See OED wild, a.4-6). Hence wild could here be tinged with the meanings of vile - 'base, vulgar, commonplace, despicable'. burthens every bough = makes every bough heavy. The imagery tends to make one think of birds sitting on boughs and singing. Every bough is crammed full with tedious birds in full song, birds more common than the nightingale. burthen, which is an old spelling of burden, also had the meaning of 'chorus, refrain'. (OED.10.) This adds an additional richness to the line. Cf. Ariel's song in The Tempest:
Come unto these yellow sands,
And then take hands:
Courtsied when you have and kiss'd
The wild waves whist,
Foot it featly here and there;
And, sweet sprites, the burthen bear.
Hark, hark!
[Burthen, dispersedly, within] Bow-wow
The watch-dogs bark!
[Burthen] Bow-wow... Tem.I.2.375-383.
There may also be a reference to the rival poets, who 'burthen every bough' with their commonplace praises of the youth.

sweets grown common = sweet things that have become common place, vulgar, widespread.
dear delight = precious and valuable ability to give pleasure. The thought is almost proverbial, although recorded proverbs do not match these words. The rarity of a thing often makes it precious

like her = like the nightingale;
sometime = at times, for some periods of time.
hold my tongue = refrain from writing verse in praise of you, or praising you in speech.

I would not = I prefer not to, I choose not to;
dull you = bore you, make you endure the tedium of my song. Also, make you lose your shine by using repetitious praise. The poet wishes to avoid the fault of over-praising the youth, which would have the effect of making all praise vulgar, dull, and as common as birdsong.