"A weak dollar is the definition of inflation."

Nope. Inflation is has to do with the value of money in terms of what you can buy. If a dollar buys 2 apples, and next week a dollar buys only 1 apple, then this decrease in purchasing power could be due to inflation.

To determine inflation they use a basket of items or what's called Consumer Price Index.

"The commonly quoted inflation rate of say 3% is actually the change in the Consumer Price Index from a year earlier. By looking at the change in the Consumer Price Index we can see that what cost an average of 9.9 cents in 1913 would cost us about $1.82 in 2003 and $2.02 in 2007."
http://inflationdata.com/inflation/Consumer_Price_Index/HistoricalCPI.aspx

Interest rates are largely dependent on the inflation rate- or more precisely the expected inflation rate in the future. If the inflation rate is 3% and a bank is charging 3% interest, the bank is obviously not making any money, and considering it has costs involved in managing money, it would be losing money. The cheapest loans one can get is called prime rate and is usually a few % above the inflation rate.

"Historically, in North American banking, the prime rate was the interest rate charged by lenders to borrowers whom they considered most creditworthy, although this is no longer the case. The prime rate varies little among banks, and adjustments are generally made by banks at the same time, although this does not happen with great frequency. The prime rate is currently 7.25% in the United States (since December 11, 2007), according to data published by The Wall Street Journal Online and the Federal Reserve Bank.[1] Canadian prime rate is currently 6.00% according to data published by Bank of Canada (as of Dec 4, 2007)."
http://en.wikipedia.org/wiki/Prime_rate

Back to first link it says:
Current Inflation Rate 3.54%

So, currently the inflation is a bit high, but generally has been bouncing around 3%

And while I'm here, the real value of gasoline with inflation adjusted dollars: