Just purchased a 2002 K1200RS, and the throttle works hard compared to all
my other bikes. Is this typical of the K bikes, or should I be looking to see if
someone put a heavier return spring on the throttle bodies??
By design, the spring on throttle-bodies are a bit stiff (1 or 2 springs depending on version and cruise-control).
EVEN MORE SO if your K1200RS is equipped with factory cruise-control. The cruise became an available "factory installed" option beginning in 2002 for USA market. In such case, there is a 2nd throttle-cable often called the "return cable" (and a 2nd spring on TB pulley).
In addition, because of the 2nd "return / push" throttle cable needed by cruise, you get the friction of both cables (hence strong spring needed). If one or both cable is old or a bit damaged / worn inside, you will get more friction over time (with age). On mine, after 8 years and 65,000 miles (around 2010), I installed brand new throttle cables of the most recent version. Nowadays, only this later "improved" version of the cables is available on BMW parts fiche. If you have custom bar-risers, you can order the K1200GT 2003-2005 throttle cables that are 1 inch longer (same design).
The new throttle cables are better designed with lower friction material inside (think it is a teflon liner) - because of this BMW says not to lube with any petrolium based product. At throttle twist-grip attach point, you can check if you see this liner inside as it is longer than needed to help friction in curved section of the cables. Older cables did NOT have this somewhat "clear" liner visible in same section (see 2nd photo..)
Furthermore, a very common problem over time (other than worn cables) is dirt that has accumulated between metal right handlebar AND plastic throttle rotating sleeve (under rubber grip). Easy to check or feel this when throttle cables are disconnected.