The fee charged for a bitcoin transaction is based off the size of the transaction (inputs and outputs). If you have a bunch of tiny inputs (tiny amounts of bitcoin) then the transaction will continue to grow in size until there is enough BTC inputs in the transaction to pay for the miners fees.
The reason the fees keep going up for you is because you continue to send tiny bits of bitcoin to solve the problem, which only makes the problem worse. You send a tiny bit, that tiny bit makes the next transaction larger, requiring a larger miners fee, resulting in an error message, so you send a tiny bit more, and the same thing happens again and again.
Think of this sort of like the difference between paying with $1 bill or 100 pennies at the supermarket…
If you pay with $1 bill, it is lightweight, and the transaction goes fast because you only have to hand over 1 dollar bill 1 time. If you pay with pennies, it is going to go slow because your going to have to hand over the pennies 1 at a time to the cashier 100 times. Both transactions are valid, but one is quick/painless ($1 dollar bill)… the other is slow/tedious and winds up costing everyone more money (pennies). Your paying with pennies bro. 
The problem can be easily solved by sending a decent amount of BTC to counterwallet. If you send 0.01 BTC, then your transaction will only require a single input, making the transaction smaller, and thereby the miners fee smaller.
The “issue” has been discussed many times in slack, on the forum here, as well as on Telegram. It is not really an issue with Counterparty or Bitcoin, but rather an issue with users not fully understanding how bitcoin transactions and miners fees work.
TL;DR… send 0.01 BTC to the wallet and try again, problem solved. 