Pairs as the big stack

[Strollen]

I understand that if you get a pp as a small stack, you need to push to an unraised pot when <10x BB. But, what
I am really confused about how to play small to mid PP. When you have a good size stack.

Say these are the hypothetical stacks

1. Hero 2200
2. Big 2600
3. Small 1000
4. Medium 1400
5. Little 800

Blinds are 100/200
Hand 1 pocket 4s
Hand 2 pocket 9s




Pocket 4s Pocket 9s
UTG Fold Push
CO raise to 500 raise to 500
Button raise to 500 raise to 500
SB (1 limper) call push
BB* fold push
*(raised to 500 from smaller stack)

But to be honest I have no clue if this is sensible or even why I'd do it this way.