I can think about different usages of "tanto" that have little to do with "a lot".
Imagine you are considering the purchase of a tool and finding a reason to spend a significant amount of money on a good quality one, rather than getting a cheap one that you are sure is of less quality. A justification, to yourself or to others, could be "Tanto lo usero' per molti anni", translated as "(I choose the good quality one for the valid reason that) I will use it for many years to come".
Another usage could be, among children trying to catch one another, is "Puoi correre veloce quanto vuoi, tanto non mi prenderai mai", translated as "You can run as fast as you can, however you will never catch me".
Another usage: "Lascia pure le scarpe a portata di mano [invece che metterle via nell'armadio] tanto usciremo ancora tra poco", translated as "Feel free to leave your shoes handy [rather than store them away] because we'll go out again shortly".
As indicated by DaG in comments, the usage you have referred to is covered by case 4.c. in treccani.it/vocabolario/tanto. To the question "Non sei andato alla riunione?", getting the answer "Tanto" would be understood as "Sarei potuto andare alla riunione; tuttavia, non sarebbe servito a nulla": I could have attended the meeting; however, it would have been pointless since it would have changed nothing in the outcome.