According to that chart 73% of benefits go towards the elderly & disabled.
While, I agree with going against abusers of the benefits, particularly welfare queens, and recent immigrants.
It's still a rather small margin of those which receive benefits.
Welfare (TANF), for example, is not an entitlement and would not be shown in your chart. Newer (legal) immigrants are often low-income and more likely to get benefits than those who have been here longer or citizens.
In 2014, 63 percent of households headed by a non-citizen reported that they used at least one welfare program, compared to 35 percent of native-headed households.
Compared to native households, non-citizen households have much higher use of food programs (45 percent vs. 21 percent for natives) and Medicaid (50 percent vs. 23 percent for natives).
Including the EITC, 31 percent of non-citizen-headed households receive cash welfare, compared to 19 percent of native households. If the EITC is not included, then cash receipt by non-citizen households is slightly lower than natives (6 percent vs. 8 percent).
New immigrants must be here a certain period of time before they are eligible although that requirement is waived for some (Cubans).
"Survey of Income and Program Participation", U.S. Census Bureau, last revised February 29, 2016.