Why and how to start lifting

Hello!

My current exercise regime consists of interval running or ellipticaling, hiking, biking, and lots of classes like TRX, barre, body pump, kickboxing, etc. Most of my resistance training thus far involves using 5 lb hand weights or body weight. My muscles are often exhausted at the end of class and sometimes sore the next day, so I feel like I am getting decent resistance training in. But I hear a lot on this forum that I should be doing heavier lifting.

Why? What kind of benefits will heavy lifting bring as opposed to what I'm currently doing? How would I start a regimine like this? The machines at the gym intimidate me, so I would have no idea which ones to start with.

Thanks in advance!