A contentious area. BUT... When partner makes a weak bid our job is to (1) help them obfuscate the opposition OR (2) try to find our own best spot.
(1) A pre-emptive weak 2 (or 3) bid is mostly designed to a nuisance. Partner will have about 6 - 9 points and a 6 card suit (the same as for a weak jump overcall).
Assuming you have no interest in game (less than 14 HCP), now what's important is FITS, i.e. do you have a fit for partner or not? And how good the fit is will determine the level you should bid at… not the point count.
[a small digression… A cornerstone of all modern bidding theory is the concept of “the level of the fit”. This theory, popularised by the US Masters Marty Bergen and Larry Cohen, though originated by a French player, states that in competitive auctions (i.e. where both sides are bidding) the combined fits of the trump suits will equal the number of tricks to be taken.
At its simplest and most raw interpretation this means that if you and partner have a 9 card fit you should contract to make 9 tricks; 10 card fit = 10 tricks etc. This is a VAST over-simplification of the theory but it nevertheless holds good in most competitive situations.
So… If partner makes a weak 2 noise and you hold 3-card support, you should therefore raise to the 3 level (6+3 =9) and with 4-card support raise to the 4 level (6+4=10). You most probably won’t make your contract but you will lose less than if they do make theirs. Theoretically. Most of the time. Percentage-wise …]
(2) If you have a very decent hand (18+) opposite a Weak Two you’ll either plump directly for game or slam or whatever. But sometimes you’ll want to know whether that Weak Two was based on a 6 count or a 9 count. You hold:
Partner opens a Weak Two in D, H, or S. If it’s 9, game is a distinct possibility in NT, H’s or S’s. But how can you know? Should you just guess? Scratch your nose? Smile apologetically and bid game anyway? NO NO NO NO NO. What you do is bid 2NT!
This says nothing about your hand but what it does do is ASK partner to tell you which end of the range the weak bid was made with. If the bid was minimum (6 - 7) the opener will just repeat the original suit and you can then decide what to do in the light of the rebid. But if partner holds a “good” hand for the opening bid partner must tell you this by bidding a “feature” in a side suit.
2S - 2NT
This says, “I’m maximum and I’ve got the club A or K.”
Armed with this valuable information you now bid the game.