When the game originally came out, it did only require a 1.6 GHz single core processor. For XP 32-bit and base game only. Since then with the patches and other add-ons released, the game's requirements have gone up. It's now recommended to have a dual-core 2.4 GHz or better to run the game. This is especially true if you are using Vista or higher, regardless of whether it's 32-bit or 64-bit.
We don't know what your system specs are, but while you may have a processor that can play the game, there may be other factors that are causing the problems. For instance, one of your mods may be doing cleanup that freezes the game temporarily. Nraas Overwatch can do this around midnight and around 4-5 am every Sim day. Also, large gardens can cause the game to temporarily freeze around 5 am game time for calculating plant updates.
Memory usage is about right. We've seen games take up to 2.5 - 3 GB memory while running, especially on 64-bit systems where the game can take up to 3.5 GB while running. Part of this is due to the large amount of resources the game takes, and part is due to the game being a 32-bit application. Allocated memory can fill up requiring swapping to the hard drive which could cause some lagging.
In short, the longer you play the game, the more "cruft" builds up in your save game file and the more resources the game needs to process the information. Adding expansions, stuff packs, store items, mods, etc. adds to the amount of resources required. As an experiment, try running the game with a brand new Sims 3 folder aka
Sims 3 Factory Reset (What & Howto) (backup your existing folder first!) and see if the game runs better without the "extras".
