How does making merit affect karma?

Sometimes merits can cancel out bad kamma, known as Ahosi Kamma. Yes good karma can cancel out some of bad karma. Good deeds with the seek for reputation, as far as I know, if someone does something with a good heart but expecting reputation as another result, it can be still merit. Because someone has to get to nirvana to stop collecting merits or kamma. Merits is a real concept. When someone does good deed even without affiliation for reputation, he will get it very soon, in this life itself.

Think of someone who gives alms to an arahat, he will receive the benefits this life itself or in the next and good results will come until he reaches Nirvana. The mind of the person who accepts alms also matters, the power of the will of the giver also matters. And Dana sila bawana are only the three main methods to get merit. There are ten methods known as Dasa Punya Kriya. Those three are the first three under the ten methods. Just search for "Ten meritorious acts".

You made a question to clear and make your view correct. When you understand the answers for the question, u collect merit. It's the number ten in the meritorious acts. And I am trying to teach you something I know on Dhamma, it is also a merit, number eight in the list.

However I will mention the ten

1. Dana
2. Sila
3. Bawana
4. Reverence
5. Services in helping others
6. Transferring merits
7. Rejoicing merits
8. Preaching dhamma
9. Listening to Dhamma
10. Straightening views

Merits a good foundation for higher levels. Without merits, you cannot continue.

When I asked this question, I did not have a good understanding of how fundamental making merit is to Buddhist practice. So it was interesting to look further into it myself.

Of all the concepts central to Buddhism, merit (puñña) is one of the least known and least appreciated in the West. This is perhaps because the pursuit of merit seems to be a lowly practice, focused on getting and "selfing," whereas higher Buddhist practice focuses on letting go, particularly of any sense of self. Because we in the West often feel pressed for time, we don't want to waste our time on lowly practices, and instead want to go straight to the higher levels. Yet the Buddha repeatedly warns that the higher levels cannot be practiced in a stable manner unless they develop on a strong foundation. The pursuit of merit provides that foundation. To paraphrase a modern Buddhist psychologist, one cannot wisely let go of one's sense of self until one has developed a wise sense of self. The pursuit of merit is the Buddhist way to develop a wise sense of self.

Merit: A Study Guide by Thanissaro Bhikkhu (quoted above) lists three activities that lead to merit; dana (giving), sila (virtue), and bhavana (meditation). This is followed by around 71 pages of sutta passages, dhammapada verses and notes that mention various aspects of merit and how important it is.

So my original question which was cynical and hinting at the fact that our motives for doing anything are rarely pure, is simply overshadowed by the fact that making merit is clearly important and holds great benefit for practitioners.

Kamma is action which produces results, which could be called "merit." It's like seeds planted in a field, no one knows for sure when they will ripen, but if they were planted, they will ripen:

Just as when seeds are not broken, not rotten, not damaged by wind & heat, capable of sprouting, well-buried, planted in well-prepared soil, and the rain-god would offer good streams of rain. Those seeds would thus come to growth, increase, & abundance.

In the same way, any action performed with greed ... performed with aversion ... performed with delusion — born of delusion, caused by delusion, originating from delusion: wherever one's selfhood turns up, there that action will ripen. Where that action ripens, there one will experience its fruit, either in this very life that has arisen or further along in the sequence.

AN 3.33

Insincere actions are those performed with greed or delusion. There's no "tricking" kamma; if you do a greedy action, the consequences are automatic, like how a person can't indulge in sensual pleasures without also becoming accustomed and attached to them in the process.

If evil has been done in the past, performing good actions now doesn't cause it to become unplanted, but developing good qualities of mind here and now means that when things ripen, you can lessen their effect.

For example, someone who meditates and keeps in mind the impermanence of all things will be less likely to be driven into rage and depression if a flood comes in and destroys their home, because this is a perfect example of that impermanence they keep reminding themselves of. They might even see the positive side that it re-affirms to them the principle of impermanence. If you don't develop good kamma right now by developing the mind, you're more likely to lose it when bad things happen.