Actually, a wood router is not heavy at all, when you compare it to better, more powerful options (spindles).

Weight is your friend, and shouldn't really affect speed if the machine is powered correctly.

You have the 3rd part backwards. The slower you go, the more likely it'll be to cause burning. The faster you cut, the cooler the bit will be, and the longer it'll last. If your machine is rigid enough, you'll find that the lack of spindle power will be the limiting factor in how fast you can go.