Not true.
Your report weight will only drop if your reports are false reports.
If you report players who are acting toxic, then your report weight wont drop since they were violating the Summoner's Code, regardless if you report once or 15 times. So long as there was actual toxic behavior happening (thus reporting for toxic behavior), then your reports will be legitimate and never lose weight.
I think you're misunderstanding how it works. If you are unfortunate enough to experience a toxic player in every game, your reports will go down if you've reported every game. Your reports will only go down if you report aimlessly towards players who are in no way violating the summoner's code.
Example: Player A was rude the entire game and called your team "bunch of retards". This can be seen as toxic behavior, so reporting him will get the match (and his account) flagged for review. Your report weight stays the same and does not decrease. The same day, Player B was also rude and called your team "bunch of autistic assholes". This is toxic, so your report is valid and flags that match for review. Even though the games were back to back, your report value does not decrease despite reporting twice. Same applies for how many reports you give in a game.
Second Example: Player A did not talk all game. You decide to report because they never talked. Your report is thrown out after the system reviews the match automatically, and your report weight is lowered. You report the next game against Player B who only said "GG", but died 8 times. Your report is tossed out again and your weight is lowered from previous weight.
I hope that makes sense. Reporting in multiple games has never decreased the value of your report, so long as the report was legitimate.