This FAQ has a complete list, (search for "cheats") but they're not in the same order as on the menu, so I can't verify that the ones I've picked out are correct. That said, I'll take a crack.
To use the cheat codes, start a career mode level and pause, and then hold Numpad 7 while you enter the code. More codes for PC are here.
The cheat might be Double Moon Physics (seems like that should come after Moon Physics, yeah?):
[Left], [Up], [Left], [Up], [Down], [Up], C, V, [Left], [Up], [Left], [Up], [Down], [Up], C, V.
The character might be Private Carrera:
Get all gaps in the game for the non-secret skate parks. It's tough.
Or cheat:
[Down], [Up], [Left], [Left], B, [Left], [Up], V, V, [Up], [Right], C, C, [Up], [Spacebar]
It looks like I have found an alternative solution. I'm using another emulator, PSXeven, and it runs the game perfectly, with CD or ISO.
I'd like to know why I'm not able to play this game using ePSXe though, since I've checked some compatibilities lists and it should work fine.
Best Answer
Based off this article https://www.ign.com/faqs/2002/tony-hawks-pro-skater-2-walkthroughfaq-367640 I'm not so sure that weight and/or durability affect anything. My thinking is that they are just stats that are there to make the "decks" feel unique.
From the article: