A quart is 2 pints. A pint is sixteen fluid ounces of water and weighs about 16 ounces (avoirdupois weight.) A gallon is 4 quarts (8 pints) and thus weighs about 8 pounds. Five gallons would be about 40 pounds.
In some cases, if your mother is on Medicaid, she can designate you as her personal home care aide and you can get paid a small amount through Medicaid. If your mother has her own resources, you can draw up a contract agreeing to work as her home health aide and she can pay you a salary that you both agree upon.
Another option: if his employer offers one, the son could open up a flexible savings account for dependent care (mom would have to be his dependent and live in his house for at least half the year). You can put in $5,000 pretax salary each year to pay for eligible dependent care expenses incurred that year.