I understand that player stats are boosted, but if you go in with a level 10 weapon does it still do only 20 damage, or does it get boosted as well?
All your stats are boosted, no matter whether they're based on your character (like health or stamina) or your actual items.
Just keep in mind that due to this items will scale similar to how your character is scaled. For example, if you're indeed level 10 and your weapon is level 5, then don't expect to have the equivalent of a level 50 weapon. It will be more likely around level 40 or even lower.
Stats do scale in Cyrodil, but it's important to remember that the system is far from perfect and doesn't scale a lot of things it probably should. For instance, I went in at lv12 on my Templar and it had me around 720 armor and resist, I'm now level 29 on my Templar and my armor/resist are both well over 900. This won't be a huge sticking point for doing the PvE content, but your contribution to PvP skirmishes will need to be either via healing, CC, or other support. Do not expect to rack up kills without outside help unless the opponent is also at or below your level. (Which will no longer be common)