Indices aren't pointless when you approach table sizes that have tens of millions of rows- and you will only see marginal improvements in query performance when dealing with the table size you are dealing with now.
You're better off leaving the indices the way they are, and reconsider your DB schema. A query shouldn't use 20+ MB of memory, and its performance will only snowball into much bigger problem as the DB grows.
That said, jumping from 70k rows to 150k rows is not a huge leap in your typical mysql database. If performance is already a concern, there is already a much larger problem at play here. If you are storing large blobs in your DB, for example, you may be better off storing your data in a file, and save its location as a varchar field in your table.
One other thing to consider, if you absolutely have to keep your DB schema exactly the way it is, is to consider partitioning your data. You can typically partition your table by ID's or datetime, and see a considerable improvement in performance.