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Why are fields more fundamental than particles?
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In quantum field theory, the field aspect and the particle aspect are 
complementary to each other (in a precise sense related to what is 
called ''second quantization''). 
 
Experimentally, depending on the experimental situation, we ''see'' 
one or the other.
 
Now one can understand the particle concept as a limit of the field 
concept, namely as the approximation of geometric optics, where particle
rays approximately follow definite paths. But there seems to be no way 
to regard the field concept as a limit of the particle concept. 
 
Moreover, a pure particle view cannot even formally capture all aspects 
of the fields. Dynamical symmetry breaking, for example, is an 
intrinsic field phenomenon.
 
Finally, even in atomic physics and quantum chemistry, electrons are 
usually delocalized - a feature naturally explained in terms of fields 
but very counterintuitive in terms of particles.
 
For all these reasons, the field aspect must be considered to be more 
fundamental.

On p.2 of his essay, 
    What is Quantum Field Theory, and What Did We Think It Is?
    http://arxiv.org/pdf/hep-th/9702027v1, 
Weinberg writes: 

''In its mature form, the idea of quantum field theory is that quantum 
fields are the basic ingredients of the universe, and particles are 
just bundles of energy and momentum of the fields. In a relativistic 
theory the wave function is a functional of these fields, not a 
function of particle coordinates. Quantum field theory hence led to a 
more unified view of nature than the old dualistic interpretation in 
terms of both fields and particles.''