I suspect you're thinking that we'd have a summer when the northern hemisphere, for example, is tilted toward the Sun, and a second summer during the perihelion, when the Earth is closest to the Sun. For one thing, the timing doesn't work; the perihelion takes place in early January, close to the northern midwinter. That probably moderates the effects of axial tilt for the northern hemisphere (and amplifies them for the southern hemisphere), but it's not enough to override them.
The other answers have said that the axial tilt is a more significant
factor than the variation in distance from the Sun, but they haven't
The following is a rough back-of-the-envelope guesstimate.
The difference in illumination caused by the varying distance from
the Sun can be computed from the ratio between the perihelion and
aphelion distance, which is about a factor of 0.967. Applying the
inverse square law indicates that amount of sunlight at aphelion is
about 93.5% of what it is at perihelion. Reference:
At my current location (about 33° north latitude), at this time of
year (close to the northern winter solstice), we're getting about 10
hours of sunlight and 14 hours of darkness each day. (Reference: the weather app on my phone.) That's about 83% of what we'd get with 12 hours of daylight during
either equinox, and about 71% of what we'd get with 14 hours of daylight and 10 hours of darkness
per day during the summer solstice. The effect is greater at higher latitudes.
In addition to that, the sun is lower in the sky during the winter
than it is during the summer, meaning that a given amount of sunlight
is spread over a larger area of the Earth's surface, which makes
the ratio even larger.
I don't have the numbers for that, but it's enough to show that the
effect of the axial tilt is substantially greater than the effect of
the varying distance between the Earth and the Sun.