Federal aid to state and local governments jumped by more than 50 percent from 1975 to 1978, to nearly $78 billion, the Treasury Department announced yesterday.

The huge increase made such grants one of the fastest growing parts of the federal budget, outstripping even the growth in Social Security benefits, and far outstripping the expansion of defense spending.

Ironically, the announcement comes as several state legislatures are considering resolutions asking Congress to call a Constitutional convention to adopt an amendment requiring a balanced federal budget. The current year's federal deficit is estimated at just over $40 billion, just over half the level of last year's aid to the states.

Because of the growing debate over the proposed amendment, Sen. Edmund Muskie (D-Maine), chairman of the Senate Budget Committee, plans to hold hearing on it in March.

The largest single aid program was for Medicaid, $10.7 billion to help poor persons pay their medical expenses.

Just over $10.5 billion was transferred to the states to cover part of the cost of unemployment benefits, training for unskilled workers, and public service employment.

The federal contribution to state welfare programs, primarily Aid to Families with Dependent Children, cost $6.3 billion, the third largest category of grants.

Payments from the Highway Trust Fund, for interstate highway construction and both construction and rebuilding of other main roads, totaled $5.7 billion.

General revenue sharing, under which the federal government gives states money for any use they please, hit $6.8 billion last year. Some members of Congress suggest that this program should be dropped on the grounds that most states' financial position is stronger than that of the federal government right now.

Other aid programs run the gamut from the school lunch program ($2.4 billion) to grants for construction of wastewater treatment plants ($3.2 billion) to elementary and secondary school assistance ($2,8 billion).

Despite the big increase in total aid to the states since 1975, there have been only small changes in each state's share of the total.

New York state received $8.4 billion last year to lead all states. That was 10.7 percent of the total. California was next with $8.0 billion, or 10.3 percent. In the last three years, aid to California has increased 63 percent.

The state of Delaware received the least, $225 million. The District of Columbia received $1.1 billion. The federal government makes a large per capita payment to the District because of the large amount of tax exempt federal property in the city.

James Davidson, chairman of the National Taxpayers Union, predicted yesterday that 12 more states would join the 22 that have already passed a resolution asking for a constitutional convention on the budget amendment.

The North Carolina legislature has made the resolution its first order of business, Davidson said. and Indiana is expected to pass it within 10 days.

Davidson praised California Gov. Jerry Brown, who last week came out for the amendment, and said NTU was trying to get him to make speeches about it across the country.