In bridge, can you tell your partner that your two bid is a weak two or a strong two as you make the bid?
No - presuming you mean during the hand after the call has been made.
OP makes no mention as to whether this is Rubber or Duplicate Bridge. However, there is great conformity between the two sets of Laws, so I will briefly outline the structure as defined in the Rubber Bridge Laws, and allow the Director of any relevant Duplicate Game to cover any extensions pertaining to that variety of the game.
The Proprieties listed in the Laws of Rubber Bridge () state:
2. Communication Between Partners
Communication between partners during the auction and play should be effected only by means of the calls and plays themselves, not through the manner in which they are made nor through extraneous remarks and gestures, nor through questions asked of the opponents and explanations given to them.
When a player has available to him improper information from his partner’s remark, question, explanation, gesture, mannerism, special emphasis, inflection, haste or hesitation, he should carefully avoid taking any advantage that might accrue to his side.
No discussion of partnership agreements or holdings is allowed during the hand. Any such would be Unauthorized Information to either partner receiving said information, penalized as in Law 16:
Law 16 – Unauthorized Information
A player may be subject to penalty if information is conveyed from his partner other than by a legal call or play.
A. Regarding information obtained from partner:
If a player conveys information to his partner by means of a remark, question, unmistakable hesitation or unwonted speed, special emphasis, tone, gesture, movement, mannerism or any other action that suggests a call, lead or plan of play, is unauthorized. When the offending side has profited by use of this unauthorized information, it should, in conformance with Proprieties 1, redress any damage done to the non-offending side.
A player on the offending side must not base any subsequent calls or plays on such unauthorized information. If it is determined that this has been violated and the non-offending side has been damaged, the result should be adjusted to redress any damage done to the non-offending side.
As regards Alerts and Announcements, the ACBL Alert Procedure states:
An announcement is one word or a short phrase which tells the opponents directly the meaning of partner's call. When bidding boxes are used, the "Alert" strip is tapped also. Announcements are required in the following instances: ...
That it is always the partner of the player making the call that performs the Announcement.
That only the specified calls that are to be Announced, and Weak Two Bids are NOT in this list (ACBL Alert Chart).
The given answer is correct to "can you tell partner which kind of 2 bid this is". But it looks like you're asking "how can I tell partner that this 2S bid is weak, and that 2S bid is strong?" You can't do that, at all, never mind telling partner which is which. There is a requirement to have a system, before the game starts, that is played through the session (and frequently, for the next 40 years).
In other words, you decide before the game what kind of 2 bids you are playing, and you don't change that during the session. You can have different "systems" at different times - for instance, playing Precision 1st and 2nd, and 2/1 if partner is a passed hand, or having 1NT be 11-13 NV, 14-16 Vulnerable; but again this must be decided in advance and not changed through the session, and definitely not after seeing your cards. A partnership system can take up hundreds of pages of agreements, or can be as simple as "Seattle 2/1, upside down carding, 1430?" (which for a pair of Seattleites can imply tens of pages of agreements!)
That's for duplicate, of course.
Rubber bridge, because it is usually cut-for-partners, tends to have a system set for the table (in many rubber bridge clubs, the club stipulates the system everyone has to play), with minimal exceptions for things like carding order. This allows everyone to know what their partner means with their bid, even if they have never played with this partner before. Again, it's one system, and each (opening, at least) bid will have a single defined meaning in a particular seat and vulnerability.