I'm not sure if pesada have got a special meaning in Perú but you can interpret it in that sentence as one of these taken from the DRAE
pesado/a
adj. Tardo o muy lento.
adj. Molesto, enfadoso, impertinente.
adj. Aburrido, que no tiene interés.
@fedorqui points
- adj. Duro, violento, insufrible, difícil de soportar.
It may be but I interpret the sentence as
La ruta es muy pesada, [porque está muy] transitada
I've highlighted the most probable one: muy lento. If the road is narrow, in bad conditions and has got high traffic, you may spend a lot of time to travel it. You move along it at a slow [lento] speed.
Either way, we can not translate it as "heavy" in that context.