The best ecological term for a weed is "ruderal".  A ruderal is a plant adapted for life on disturbed soil.  Ruderals grow fast, a property that depends heavily on readily available forms of plant nutrients.  For example, nitrogen tied up in organic form is not of much use to ruderals; they need soluble nitrate to realize their fast growth rates.  Other components of the ruderal strategy are high reproductive rates and independence of symbiotic fungi.  In other words most ruderals, at least in arid climates, do not need to become mycorrhizal.  

These traits make ruderals very well suited for life on disturbed sites and newly graded soil, exactly the places where restoration projects are planted.  Slower-growing native plants on the other hand do not benefit from these characteristics and must find mycorrhizal symbionts in the soil if they are to survive.  Nitrate and other readily available forms of plant nutrients are of no particular advantage to natives, which get along on very slowly released forms of nutrients in their native habitats.  

The differences in optimum soil conditions are only some of the factors that select for either late successional natives or ruderals.   The network of mycorrhizal fungi exerts an effect of its own on many ruderal plant species.  In the case of Russian thistle, the mycorrhizal fungi behave almost as pathogens, causing death of the ruderal plant's roots.  Other ruderal species do not react in quite such a dramatic way, but most cannot grow rapidly in the presence of a well-developed mycorrhizal network.  The mechanisms are not understood, but a number of experiments have demonstrated the effect.  See the restoration project section of this web site for examples from practical projects.