It is not uncommon for games to only allow a "new game plus" on the difficulties which you have bested.
Your question hints you've only completed the game on normal. If so, you will not be able to carry all your weapons to professional, but will instead need to beat professional from scratch before being able to do that. If you were to try a new game in normal difficulty, you would be able to carry everything over. This is affirmed by the following FAQ, specifically:
(Q) Why can't I start Professional
mode with all my weapon upgrades?
(A) You have to start a new game when
first starting Professional mode, so
all the upgrades that were obtained
on a previous normal save will not
carry over. Be sure to save your
Professional mode bonus game once
Professional mode is completed.
The same FAQ states the way to unlock the infinite rocket launcher:
-- Infinite Rocket Launcher
Complete the main game and the
merchant will sell it for 1000000
pesetas in the bonus game of Leon's
main game on any difficulty.
Though it is not 100% clear whether that means that this unlockable will be available for purchase on all difficulties, or only on difficulties which you have finished once. Another quote hints that it is the latter:
(Q) Can I use my unlocked weapons on
any mode? For instance, can I unlock
the P.R.L. 412 on Professional and
use it on normal mode?
(A) Yes. Just make sure to keep a
bonus game saved for each difficulty.
This is fairly easy to find out, however. Just get to the merchant on Professional and see if he has this.