Each block generates a reward. All money stems from this. Your wallet is just slivers from such blocks. When you send money it takes such a sliver and send one sliver to where you wanted it and you keep the other. BUT, if you want to send more than you have in a sliver then you need to send a whole sliver and then a sliver from another chunk. The resulting transaction is larger and therefor it costs more money.

Sending more money does not cost more, per se. But it makes it more likely that you need to use more slivers thereby making a bigger transaction.

Sometimes exchanges clean up their dust, it is called. The process consists of taking a ton of slivers and send them to themselves making them into one big sliver and that makes future transactions cheaper.