As a not-svelte person, my first reaction to this announcement was negative. However, it is perfectly legal. FLSA regulations allow an employer to use any "bona fide occupational qualifications" (BOQs) to determine job eligibility. Functional job requirements are always spelled out as part of the job description. Functional requirements of bedside nursing jobs
include lifting, walking, bending, standing, etc..... and these are simply not possible with a very high BMI. As long as the requirements are tied to BOQs and applied to everyone who is hired - it doesn't seem to violate FLSA.
On a personal note whenever I have had to pick up the slack for co-workers who couldn't (or wouldn't) perform some tasks it felt OK when the cause was associated with something of a limited duration (ex: stumping along on a walking cast) but much less tolerable if there was no end in sight. It created resentment and poor morale on the part of those left with the extra work.
It is interesting that this is being associated with race discrimination. Victoria is only 90 miles away from Houston - which is the most diverse city in the US according to the latest census data.