In bridge, can you tell your partner that your two bid is a weak two?
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: ...


Note:


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).