Sen. John Heinz (R-Pa.) last year became one of the most prolific letter senders in history. He mailed 15 million pieces, three for every household in Pennsylvania.

It didn't cost Heinz, a multimillionaire who was up for reelection, a dime. Like every senator, he has almost unlimited free use of the mails for "official business" under the congressional franking privilege. So taxpayers footed his mailing bill at an estimated cost of $2.25 million.

Heinz' Democratic opponent, Cyril H. Wecht, raised only $4l7,539 for his campaign, or less than one-fifth the amount taxpayers spent on Heinz' election-year newsletters.

Heinz was by no means alone. Last year, the 100 U.S. senators sent a record 234 million pieces of mail, or almost three per household nationwide, at a cost to taxpayers of more than $48 million in postage and paper.

Only 4 percent of these mailings were replies to questions from constituents. The rest were newsletters, press releases and other self-promoting announcements. Newsletters alone accounted for 214 million pieces.

Not surprisingly, the biggest mailers, according to a report prepared for the Senate Rules Committee, were from the nation's most populous states. The top five last year were Heinz, Sens. Alfonse M. D'Amato (R-N.Y.), Charles H. Percy (R-Ill.), Lloyd Bentsen (D-Tex.) and Daniel Patrick Moynihan (D-N.Y.).

D'Amato sent 14.4 million pieces of mail; Percy, 13.5 million; Bentsen, 11.8 million, and Moynihan, 11.6 million. Their mailings cost taxpayers $9.9 million. Heinz, Bentsen and Moynihan were up for reelection and won.

The amount of use of the frank by members has long been a well-kept secret. The Rules Committee study is the first senator-by-senator accounting in recent history.

The committee, which is expected to act on several modest cost control measures on Senate mailing next week, refuses to release the list, fearing it would embarrass some senators.

The list, according to numerous sources, reveals that 10 senators accounted for almost half the mail sent from the Senate and the greatest use of the frank was by senators seeking reelection.

The second top five mailers were Donald W. Riegle Jr. (D-Mich.), with 10.9 million pieces; John P. East (R-N.C.), 8.5 million; Carl Levin (D-Mich.), 6.9 million; Lawton Chiles (D-Fla.), 6.4 million, and Roger W. Jepsen (R-Iowa), 5.8 million.

Senators claim newsletters are a valuable way to communicate with constituents.

"I believe some of the most important legislative efforts I have made in my 22 years have been those least noted by the press," said Sen. Claiborne Pell (D-R.I.). ". . . My constituents have been informed of these efforts through newsletters."

Critics, however, contend that newsletters are little more than election propaganda.

"The frank gives incumbents access to the federal treasury for reelection purposes," said Ellen Block, a lawyer for Common Cause, a self-styled citizens lobby.

Often the newsletters are hard to distinguish from campaign literature. Heinz' August newsletter, for example, included four pictures of him and a host of headlines directed at major campaign issues.

"Getting Pennsylvania Working Again," said one. "Securing Social Security," said another. "Helping Unemployed Americans," said a third. The first page of the newsletter alone carried 12 references to Heinz.

The study also looked at the number of letters sent per mailbox in each state. On this basis, some senators from smaller states make Heinz look like a piker.

Sen. George J. Mitchell (D-Maine) was the leader here, mailing the equivalent of seven letters to each mailbox in the state during his reelection campaign.

Senate Minority Leader Robert C. Byrd (D-W.Va.), also up for reelection, was second with six to each mailbox. Sen. Howard W. Cannon (D-Nev.), who was defeated, Jepsen, Ted Stevens (R-Alaska) and Quentin N. Burdick (D-N.D.) each sent more than five letters to every mailbox in their states.

Iowa's two Republican senators, Jepsen and Charles E. Grassley, neither of whom faced reelection in 1982, sent a total of 11.3 million pieces of mail, or more than 10 per household in the Cornhusker state.

Delaware's two senators, William V. Roth Jr., a Republican, and Joseph R. Biden Jr., a Democrat, together sent the equivalent of eight pieces of mail to each household in the state. Other big mailers were Sens. Jim Sasser (D-Tenn.), Larry Pressler (R-S.D.), and John Melcher (D-Mont.).

Sasser, whose state has only 1.6 million mailboxes, sent 6 million newsletters in 1981 and two million last year, according to press spokesman Doug Hall. East mailed 6.2 million letters between Sept. 9 and Oct. 29 at a cost of $1.4 million.

Senate mass mailings have grown by leaps and bounds in recent years, causing postal costs to skyrocket. In 1979, senators sent 93 million pieces. This rose to 118 million in 1980, an election year, 142 million in 1981 and 214 million in 1982, another election year.

Newsletters make up three-fourths of these mailings, said Senate Rules Committee Chairman Charles McC. Mathias Jr. (R-Md.). "These are written by our office staffs, printed for us by the Senate Service Department, addressed for us with labels printed by the Senate Computer Center from computerized mailing lists tapes we obtain, and mailed for us by the service department, usually at the third-class postage rate of 9.3 percent."

East, an outspoken conservative, was not up for reelection last fall. But copies collected by the North Carolina Democratic Party show the newsletters he sent during the campaign were full of praise for his ally, Sen. Jesse Helms (R-N.C.), and critical of "liberal North Carolina newspapers," "the Panama Canal Giveaway," "Red China," "liberal foreign aid giveaways," the NAACP, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), and "the liberals in Congress."

One newsletter said the Voting Rights Act was "part of a liberal effort to rig the electoral process to suit their desires and their pet causes. The liberals behind the so-called Voting Rights Act want racial minorities to hold office in direct proportion to their number--a kind of affirmative action program or quota system for elected officials!"

Under House rules, each member can send six mailings annually to every household in his or her district. Senators can send an unlimited number of letters.

Each Senate newsletter must be mailed to a specific address while House letters are sent to "postal patrons." As a result, thousands of the Senate pieces are returned unopened because they had incorrect addresses.

Undelivered letters cost the Senate about $3 million last year, or 20 cents each.

Mathias has proposed that each senator be advised of his or her mailing costs, which is not now done; that the Senate consider mail on "a postal patron" basis; that new restrictions be put on paper allotments, and that limits be put on address files. CAPTION: Picture, Sen. John Heinz, a multimillionaire, sent 15 million pieces of mail to his constituents last year, the most mailed by any senator. He used franking priviliges, costing taxpayers about $2.2 million.