Have an arborist examine the tree for signs of disease and identify the core reasons for the balance issues.
Have a professional, large-tree pruning expert look at the branches and discuss trimming the tree with the arborist. If they agree that the tree can be saved in that location with trimming, plan to remove excessively heavy branches and evenly distribute weight around the tree's center. Cut cross-branches to allow wind to pass through the tree as opposed to pushing against the tree and toppling it.
Trim the tree according to plan so that one side doesn't become heavier than the other side, leading to toppling risk. Most large trees should only be trimmed by a licensed professional.
Excavate areas for construction by hand when dealing with large trees. You can do this yourself or hire day laborers to expedite the process. Rather than using large machines that would cut away roots, hand excavation helps preserve root bases to mitigate the possible root loss.
Nourish the soil with a layer of mulch around the base over root distribution areas; provide adequate water when the surrounding landscape dramatically changes as in city roads and sidewalk construction. A 2- to 4-inch layer of mulch is enough to provide nutrients and won't prevent water from passing through.