In the question, you have stated several false and-or dubious claims:
Copper is lightweight
Copper is more dense ("heavier") than all of the three listed alternatives; it has density of 8.9 g/cm3, which is higher than aluminum (2.7 g/cm3), steel (7.7 to 8.1 g/cm3) and titanium (4.5 g/cm3).
Copper is the best heat conducter [sic] you can get
There actually are better heat conductors than copper, they are just not applicable: for example silver (expensive), diamond (prohibitively expensive and challenging to machine into shapes resembling cookware), boron arsenide (used for cooling systems of electronic components; while arsenic itself is highly toxic and carcinogenic, boron arsenide is supposedly inert and non-toxic, but brittle and difficult to machine, and even if it was possible to make cookware from it, I wouldn't trust it). What is more, thermal conductivity does not really matter that much in cooking because the limiting factor for cooking speed is the amount of heat generated per time unit by the burner, not the thermal conductivity of the cookware. This is not an overclocked processor nor a nuclear reactor, just an ordinary gas burner with a metal pot.
Copper seems to not cause any risk to health
Please do at least minimum amount of research before asking questions on SE. A quick few-minutes-long read on Wikipedia proves that it is not true. It is an essential element and is not hyper-toxic (you won't drop dead after eating a single dish cooked in copper pot), but excess intake causes a wide range of adverse effects, so yes, copper can definitely harm one's health.
Copper is not that reactive, but nonetheless it can slowly leach from the cookware into foods and liquids being cooked. Low pH and presence of anions such as chloride facilitates this process.
One of the reasons is that pure copper is soft and mechanically inferior to the listed alternatives, especially steel. What it more, water-soluble copper salts have an unpleasant bitter taste, so besides toxicity risks, they can also adversely affect taste of the food and fluids being cooked in the pot.