Why sukha (third Jhana) is more refine than pīti (second Jhana)?

Sukha can come before piti.

Try it yourself.

Go directly into the third jhana, stay there, then go into the second jhana. In this way sukha will be before piti.

If you're asking why the jhanas follow in such order so that piti naturally comes before sukha, it is because of layers of ignorance.

The more to the surface of meditation the more you experience. (or The more ignorance, the more you experience)

The deeper you go into meditation the less you experience. (or The less ignorance, the less you experience)

Thus, in Jhana meditation you are getting rid of ignorance and that's why piti comes naturally before sukha.

Why exactly piti comes naturally before sukha?

Because of kamma.

Kamma defines our ignorance.

Ignorance defines the natural order of Jhanas.

In the third jhana equanimity arises, this is neither a pleasant nor painful feeling. This 'neutral' feeling goes beyond pleasant feeling and mental satisfaction of pleasant feeling (Piti and sukha). Equanimity is pleasantness of a different variety to the material world, a pleasantness which has surpassed the feeling of the material world, but cannot be said to be pleasant feeling as it essential does not reside in the physical plane.

Try not to attribute piti and sukha with any certain jhana. Leading up to the first jhana body is surmounted (which feels relaxing), in the first jhana feeling is surmounted (which feels pleasant), in the second mind is surmounted (which feel like mental calm), in the third mind objects are surmounted (which feels releasing), in the fourth the entire physical experience is surmounted (which feel liberating). These are the four foundations of mindfulness which stack up on one and other as you move through to the fourth.

'mindfulness of breath supports the four foundations, the four foundations support the seven factors'

'Purity of mindfulness due to equanimity' (fourth jhana)

Upasaka Sarath, two thing come to mind that might be supportive to dispel doubt and give rise to clearency:

One is the chain of "depending co-dissapearing", "lokuttara depending co-arising": jāti -> dukkha -> saddha -> pāmujja -> pīti -> passaddhi -> sukha -> samādhi ... (see SN12.23 or AN 10.1 which shows the same pattern, so to see that it's not a onetime issue.

And the other is, that in origin countries (traditional) pīti is not translated as rapture or joy like in english, but with words equal "satisfied" or gratified, like if have eaten enough (which makes also the chain above more understandable, and does not require to develop philosophical theories of what the different between "joy" and "pleasure" might be.

Maybe that "short-cut" brings sufficent satisfaction, gatification, or was final dish for pīti to simply follow further the chain.

(Note: This answer is a gift of Dhamma an not meant ro use for commercial purposes or other wordily gains.)

Joy is still an emotion, it has an element of excitement. Sukkha, is just peaceful satisfaction, "everything is right".

Joy makes you tired. It shifts you off-balance. You can be a bit drunk with joy, so joy is still an intoxicant, an asava.

Sukkha is stable. It has it's problems too, it's own limits, but it's way more sober than joy. When you're emotionally sober, you can see things much more clearly, you can act with more skill.

However, cultivating Joy is considered a prerequisite, because you need to learn to control your brain chemistry before you proceed with advanced vipashyana practice.

Lesser khandha = Stable mind state = Better happiness.

Vitakka, vicāra, pīti, and sukkha are acceleration of consciousness to access jhāna. the practitioner need them to develop jhāna-consciousness, until he turn to be professor in each jhāna. After that they become an obstruction of jhāna's stability.

Too many cooks spoil the broth.