We have a large vegetable garden.

weeds eventually grow throughout the garden, and of course need to be
removed, which is a tedious job.

I don't know where the weeds come from, but they only grow in the
garden, and they grow fast.

If we built a greenhouse on half of the garden, will the weeds from
outside of the garden spread easily into the garden? would the weeding
job be easier? let's assume that once it is planted, the tools are only
used inside the greenhouse and there is little walking between the
greenhouse and the open areas.

in other words, will a screen protect the weeds from spreading? I
assume it is airborn somehow.

dave