According to Ozhegov's dictionary, the basic literal meaning of тугой is "taut", "pulled tight", "stiffly elastic", "stretched to its limits", etc.

Thus, a properly inflated basketball could be called a тугой мяч; a stiff metal spring (but not a Slinky!) would be a тугая пружина. A тугой чемодан is an overstuffed suitcase. And a wealthy man may be said to have a тугой кошелёк -- a wallet so fat it's about to split open.

P.S. Although тугой can be used to describe a spring (пружина), or other things that are physically elastic (упругий), the phrase тугой человек does NOT mean someone "with a mind like a steel trap"! (о том, у кого ум быстр, как стальной капкан на пружине)

Quite the opposite, in fact -- if you say тугой figuratively about a person, it means a "slow thinker".