Verse 1 lists what the speaker has not done, verse 2 what he has done instead, verse 3 tells Israel to do the same. The three denials of verse 1 are ordered from the inside out, גָבַהּ (ga-vah, v.1) of the heart, רָמוּ (ra-mu, v.1) of the eyes, then walking, so ambition is tracked from where it starts to where it becomes visible. The last two words of verse 1, וּבְנִפְלָאוֹת (uv-nif-la-ot, v.1) and מִמֶּנִּי (mi-me-ni, v.1), are the pivot: the objection is not that great things are bad but that these particular ones are beyond this particular person. Verse 3 then makes the point that the psalm is not about modesty as a private virtue. Waiting is the collective form of the same discipline, and the psalm ends on for ever, which is the longest wait available.
Verse 2 opens with אִם (im, v.2) and לֹא (lo, v.2), literally if not, which is the second half of a Hebrew oath with the curse left unsaid: if I have not stilled my soul, then may such and such happen to me. Translations render it surely, and the force is a sworn statement rather than a hesitation. The verb שִׁוִּיתִי (shi-vi-ti, v.2) is from the root meaning to be level or even, so the soul is not suppressed but flattened out, brought to the same height everywhere. The comparison itself is disputed in one respect. A weaned child is past the age of crying for the breast, so most read the image as contentment without demand; others hear the recent loss in it, a child who has been weaned and has stopped protesting. The Hebrew supports both, and the difference matters, because one reading gives peace and the other gives resignation.
The heading says of David, and the psalm denies exactly the things a king's life is made of. Whether the heading marks authorship, dedication or a style of psalm is an old question and the Hebrew preposition does not settle it, but the tension is on the page either way. The placement in the collection sharpens it further: the psalm that follows is the long one about David's oath not to sleep until he has found a place for the ark, which is precisely walking among great things. Read as a pair, 131 and 132 give the two halves of one posture, no ambition for oneself and total ambition for the house. The command of verse 3 is also the standard reading of the whole book of Psalms in miniature, since waiting rather than achieving is what most of the collection asks for.
The image in verse 2 is the closest the Psalter comes to describing the soul in a state of receiving nothing and being at rest anyway. A nursing child takes; a weaned child stays. The mystical reading treats that as the whole discipline: the relation is not sustained by what is being supplied, and the soul that has stopped drawing has not stopped being held. כַּגָּמֻל (ka-ga-mul, v.2) repeats the comparison with the definite article, that same weaned child, and puts it on me, so the speaker who quieted his soul is now the mother in his own image. Verse 3 extends the same picture to a nation, and the two words at the end, from now and for ever, are a formula that closes several of the Songs of Ascents. The state described is not a moment reached once but a position held.