Ask Mr. Smarty Plants

Yes, take the weeping willow down. Non-native to the United States, Salix x sepulcralis is a hybrid of a Chinese species (Peking willow) and a European species (white willow), and is said to grow in Zones 5 to 8 in the United States. It is weak-wooded, fast-growing and, therefore, short-lived. It has aggressive roots, can lift sidewalks and interfere with sewer lines, often growing on soil surfaces, making a problem with mowing. It is susceptible to a number of pests and diseases, and notorious for littering the ground beneath it. You might check out this University of Florida Extension website on Weeping Willows for more information as well as this Q&A from North Dakota State University Extension on weeping willows.

Given the choice between a lovely native tree like Magnolia virginiana (Sweetbay) and the invasive, non-native weeping willow, we would definitely vote for the magnolia. A 13-ft. tall magnolia would be a challenge to transplant, and you might very well lose it in the process. Then, when the weak, short-lived willow dies, you will have zero trees instead of two. The magnolia will mature to from 12 to 20 ft. in height, and up to 50 ft in the southern part of its range. Since Anne Arundel County is in USDA Hardiness Zone 7a, we feel you could depend on the tree getting taller.

Here are the growing conditions for the Sweetbay Magnolia:

Growing Conditions

Water Use: High
Light Requirement: Part Shade
Soil Moisture: Moist
Soil pH: Acidic (pH<6.8)
CaCO3 Tolerance: None
Soil Description: Rich, moist soils. . Sandy, Sandy Loam, Medium Loam, Clay Loam, Clay, Acid-based
Conditions Comments: Sweetbay is slow-growing and has no serious disease or insect problems. It is good for a small patio or specimen tree. Prune after blooming during the growing season because dormant magnolias do not easily heal.

If you are determined to go ahead with moving the magnolia, here is an article from University of Tennessee on Transplanting Trees.  Frankly, we would engage a professional, licensed arborist, with proper equipment and manpower, who could have more success with the move. The same goes with removing the willow, as your first priority is to NOT harm your magnolia.

From our Native Plant Image Gallery:

Magnolia virginiana

Magnolia virginiana

Magnolia virginiana